In[1]:= fiBL[x_,z_] = (1-x/h)(1-z/h)

             x       z
Out[1]= (1 - -) (1 - -)
             h       h

In[2]:= fiBR[x_,z_] = (x/h)(1-z/h)

               z
        x (1 - -)
               h
Out[2]= ---------
            h

In[3]:= fiTR[x_,z_] = (x/h)(z/h)

        x z
Out[3]= ---
         2
        h

In[4]:= fiTL[x_,z_] = (1-x/h)(z/h)

             x
        (1 - -) z
             h
Out[4]= ---------
            h

In[5]:= psiL[x_,z_] = 1 - x/h

            x
Out[5]= 1 - -
            h
In[6]:= psiR[x_,z_] =  x/h

        x
Out[6]= -
        h

In[7]:= psiB[x_,z_] = 1 - z/h

            z
Out[7]= 1 - -
            h

In[8]:= psiT[x_,z_] =  z/h

        z
Out[8]= -
        h

In[9]:= Integrate[fiBL[x,z]  fiBL[x,z], {x, 0, h}, {z, 0 , h}]

         2
        h
Out[9]= --
        9

In[11]:= Integrate[fiBR[x,z]  fiBL[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[11]= --
         18


In[12]:= Integrate[fiTR[x,z]  fiBL[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[12]= --
         36


In[13]:= Integrate[fiTL[x,z]  fiBL[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[13]= --
         18


In[14]:= Integrate[psiL[x,z]  fiBL[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[14]= --
         6


In[15]:= Integrate[psiR[x,z]  fiBL[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[15]= --
         12


In[16]:= Integrate[fiBR[x,z]  fiBR[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[16]= --
         9


In[17]:= Integrate[fiTR[x,z]  fiBR[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[17]= --
         18


In[18]:= Integrate[fiTL[x,z]  fiBR[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[18]= --
         36



In[19]:= Integrate[psiL[x,z]  fiBR[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[19]= --
         12


In[20]:= Integrate[psiR[x,z]  fiBR[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[20]= --
         6


In[21]:= Integrate[fiTR[x,z]  fiTR[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[21]= --
         9


In[22]:= Integrate[fiTL[x,z]  fiTR[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[22]= --
         18


In[23]:= Integrate[psiL[x,z]  fiTR[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[23]= --
         12


In[24]:= Integrate[psiR[x,z]  fiTR[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[24]= --
         6


In[25]:= Integrate[fiTL[x,z]  fiTL[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[25]= --
         9


In[26]:= Integrate[psiL[x,z]  fiTL[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[26]= --
         6


In[27]:= Integrate[psiR[x,z]  fiTL[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[27]= --
         12


In[28]:= Integrate[psiB[x,z]  fiBL[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[28]= --
         6


In[29]:= Integrate[psiT[x,z]  fiBL[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[29]= --
         12


In[30]:= Integrate[psiB[x,z]  fiBR[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[30]= --
         6


In[31]:= Integrate[psiT[x,z]  fiBR[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[31]= --
         12


In[32]:= Integrate[psiB[x,z]  fiTR[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[32]= --
         12


In[33]:= Integrate[psiT[x,z]  fiTR[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[33]= --
         6


In[34]:= Integrate[psiB[x,z]  fiTL[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[34]= --
         12


In[35]:= Integrate[psiT[x,z]  fiTL[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[35]= --
         6


In[36]:= Integrate[psiL[x,z]  psiL[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[36]= --
         3



In[37]:= Integrate[psiR[x,z]  psiL[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[37]= --
         6


In[38]:=  Integrate[psiR[x,z]  psiR[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[38]= --
         3

In[39]:= Integrate[psiB[x,z]  psiB[x,z], {x, 0, h}, {z, 0 , h}]

          2
         h
Out[39]= --
         3


In[40]:= dxfiBL[x_,z_] = D[fiBL[x,z],x]

               z
           1 - -
               h
Out[40]= -(-----)
             h


In[41]:= dzfiBL[x_,z_] = D[fiBL[x,z],z]

               x
           1 - -
               h
Out[41]= -(-----)
             h


In[42]:= dxfiBR[x_,z_] = D[fiBR[x,z],x]

             z
         1 - -
             h
Out[42]= -----
           h


In[43]:= dzfiBR[x_,z_] = D[fiBR[x,z],z]

           x
Out[43]= -(--)
            2
           h


In[44]:= dxfiTR[x_,z_] = D[fiTR[x,z],x]

         z
Out[44]= --
          2
         h


In[45]:= dzfiTR[x_,z_] = D[fiTR[x,z],z]

         x
Out[45]= --
          2
         h


In[46]:= dxfiTL[x_,z_] = D[fiTL[x,z],x]

           z
Out[46]= -(--)
            2
           h

In[47]:= dzfiTL[x_,z_] = D[fiTL[x,z],z]

             x
         1 - -
             h
Out[47]= -----
           h


In[48]:= dxpsiL[x_,z_] = D[psiL[x,z],x]

           1
Out[48]= -(-)
           h

In[49]:= dxpsiR[x_,z_] = D[psiR[x,z],x]

         1
Out[49]= -
         h

In[50]:= dzpsiB[x_,z_] = D[psiB[x,z],z]

           1
Out[50]= -(-)
           h

In[51]:= dzpsiT[x_,z_] = D[psiT[x,z],z]

         1
Out[51]= -
         h

*****************for a_11 ***************

In[52]:= Integrate[dxfiBL[x,z] dxfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[52]= -
         3

In[53]:= Integrate[dzfiBL[x,z] dzfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[53]= -
         3

*****************for a_12 ***************


In[54]:= Integrate[dxfiBR[x,z] dxfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[54]= -(-)
           3


In[55]:= Integrate[dzfiBR[x,z] dzfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[55]= -
         6

*****************for a_13 ***************

In[56]:= Integrate[dxfiTR[x,z] dxfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[56]= -(-)
           6

In[57]:= Integrate[dzfiTR[x,z] dzfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[57]= -(-)
           6

*****************for a_14 ***************

In[58]:= Integrate[dxfiTL[x,z] dxfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[58]= -
         6


In[59]:= Integrate[dzfiTL[x,z] dzfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[59]= -(-)
           3

*****************for a_15 ***************

In[60]:= Integrate[dzfiBL[x,z] dxfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[60]= -
         4


In[61]:= Integrate[dxfiBL[x,z] dzfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[61]= -
         4

*****************for a_16 ***************

In[62]:= Integrate[dzfiBR[x,z] dxfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[62]= -
         4

In[63]:= Integrate[dxfiBR[x,z] dzfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[63]= -(-)
           4

*****************for a_17 ***************

In[64]:= Integrate[dzfiTR[x,z] dxfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[64]= -(-)
           4


In[65]:= Integrate[dxfiTR[x,z] dzfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[65]= -(-)
           4

*****************for a_18 ***************

In[66]:= Integrate[dzfiTL[x,z] dxfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[66]= -(-)
           4

In[67]:= Integrate[dxfiTL[x,z] dzfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[67]= -
         4

************************* for a_19 *******************

In[68]:= Integrate[dxpsiL[x,z] dxfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[68]= -
         2

************************* for a_1,10 *******************

In[69]:= Integrate[dxpsiR[x,z] dxfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[69]= -(-)
           2

************************* for a_1,11 *******************

In[70]:= Integrate[dzpsiB[x,z] dxfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[70]= -
         2

************************* for a_1,12 *******************


In[71]:= Integrate[dzpsiT[x,z] dxfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[71]= -(-)
           2

************************ for a_22 *******************
In[72]:= Integrate[dxfiBR[x,z] dxfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[72]= -
         3

In[73]:= Integrate[dzfiBR[x,z] dzfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[73]= -
         3

************************  For a_23 ****************************

In[74]:= Integrate[dxfiTR[x,z] dxfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[74]= -
         6


In[75]:= Integrate[dzfiTR[x,z] dzfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[75]= -(-)
           3

************************  For a_24 ****************************

In[76]:= Integrate[dxfiTL[x,z] dxfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[76]= -(-)
           6

In[77]:= Integrate[dzfiTL[x,z] dzfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[77]= -(-)
           6


************************  For a_25 ****************************


In[78]:= Integrate[dzfiBL[x,z] dxfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[78]= -(-)
           4

In[79]:= Integrate[dxfiBL[x,z] dzfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[79]= -
         4

************************  For a_26 ****************************

In[80]:= Integrate[dzfiBR[x,z] dxfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[80]= -(-)
           4

In[81]:= Integrate[dxfiBR[x,z] dzfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[81]= -(-)
           4

************************  For a_27 ****************************

In[82]:= Integrate[dzfiTR[x,z] dxfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[82]= -
         4

In[83]:= Integrate[dxfiTR[x,z] dzfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[83]= -(-)
           4


************************  For a_28 ****************************

In[84]:= Integrate[dzfiTL[x,z] dxfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[84]= -
         4

In[85]:= Integrate[dxfiTL[x,z] dzfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[85]= -
         4
************************  For a_29 ****************************
In[86]:= Integrate[dxpsiL[x,z] dxfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[86]= -(-)
           2

************************  For a_2,10 ****************************

In[87]:= Integrate[dxpsiR[x,z] dxfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[87]= -
         2


************************  For a_2,11 ****************************

In[88]:= Integrate[dzpsiB[x,z] dxfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[88]= -(-)
           2

************************  For a_2,12 ****************************

In[89]:= Integrate[dzpsiT[x,z] dxfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[89]= -
         2

************************  For a_33 ****************************

In[90]:= Integrate[dxfiTR[x,z] dxfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[90]= -
         3

In[91]:= Integrate[dzfiTR[x,z] dzfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[91]= -
         3

************************  For a_34 ****************************

In[92]:= Integrate[dxfiTL[x,z] dxfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[92]= -(-)
           3

In[93]:= Integrate[dzfiTL[x,z] dzfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[93]= -
         6

************************  For a_35 ****************************

In[94]:= Integrate[dzfiBL[x,z] dxfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[94]= -(-)
           4

In[95]:= Integrate[dxfiBL[x,z] dzfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[95]= -(-)
           4

************************  For a_36 ****************************

In[96]:= Integrate[dzfiBR[x,z] dxfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

           1
Out[96]= -(-)
           4

In[97]:= Integrate[dxfiBR[x,z] dzfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[97]= -
         4
************************  For a_37 ****************************

In[98]:= Integrate[dzfiTR[x,z] dxfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[98]= -
         4

In[99]:= Integrate[dxfiTR[x,z] dzfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

         1
Out[99]= -
         4

************************  For a_38 ****************************

In[100]:= Integrate[dzfiTL[x,z] dxfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[100]= -
          4

In[101]:= Integrate[dxfiTL[x,z] dzfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[101]= -(-)
            4

************************  For a_39 ****************************
In[102]:= Integrate[dxpsiL[x,z] dxfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[102]= -(-)
            2

************************  For a_3,10 ****************************

In[103]:= Integrate[dxpsiR[x,z] dxfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[103]= -
          2

************************  For a_3,11 ****************************

In[104]:= Integrate[dzpsiB[x,z] dxfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[104]= -(-)
            2

************************  For a_3,12 ****************************

In[105]:= Integrate[dzpsiT[x,z] dxfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[105]= -
          2


************************  For a_44 ****************************


In[106]:= Integrate[dxfiTL[x,z] dxfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[106]= -
          3

In[107]:= Integrate[dzfiTL[x,z] dzfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[107]= -
          3

************************  For a_45 ****************************

In[108]:= Integrate[dzfiBL[x,z] dxfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[108]= -
          4

In[109]:= Integrate[dxfiBL[x,z] dzfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[109]= -(-)
            4

************************  For a_46 ****************************

In[110]:= Integrate[dzfiBR[x,z] dxfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[110]= -
          4

In[111]:= Integrate[dxfiBR[x,z] dzfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[111]= -
          4

***********************  For a_47 ****************************

In[112]:= Integrate[dzfiTR[x,z] dxfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[112]= -(-)
            4

In[113]:= Integrate[dxfiTR[x,z] dzfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[113]= -
          4

***********************  For a_48 ****************************

In[114]:= Integrate[dzfiTL[x,z] dxfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[114]= -(-)
            4

In[115]:= Integrate[dxfiTL[x,z] dzfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[115]= -(-)
            4

***********************  For a_49 ****************************

In[116]:= Integrate[dxpsiL[x,z] dxfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[116]= -
          2

***********************  For a_4,10 ****************************


In[117]:= Integrate[dxpsiR[x,z] dxfiTL[x,z] , {x, 0, h}, {z, 0 , h}]      

            1
Out[117]= -(-)
            2

***********************  For a_4,11 ****************************

In[118]:= Integrate[dzpsiB[x,z] dxfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[118]= -
          2

***********************  For a_4,12 ****************************

In[119]:= Integrate[dzpsiT[x,z] dxfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[119]= -(-)
            2

***********************  For a_59 ****************************

In[120]:= Integrate[dxpsiL[x,z] dzfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[120]= -
          2

***********************  For a_5,10 ****************************

In[121]:= Integrate[dxpsiR[x,z] dzfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[121]= -(-)
            2

***********************  For a_5,11 ****************************

In[122]:= Integrate[dzpsiB[x,z] dzfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[122]= -
          2

***********************  For a_5,12 ****************************

In[123]:= Integrate[dzpsiT[x,z] dzfiBL[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[123]= -(-)
            2


**********************  For a_6,9 ****************************

In[124]:= Integrate[dxpsiL[x,z] dzfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[124]= -
          2

**********************  For a_6,10 ****************************

In[125]:= Integrate[dxpsiR[x,z] dzfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[125]= -(-)
            2

**********************  For a_6,11 ****************************

In[126]:= Integrate[dzpsiB[x,z] dzfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[126]= -
          2

**********************  For a_6,12 ****************************

In[127]:= Integrate[dzpsiT[x,z] dzfiBR[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[127]= -(-)
            2

**********************  For a_7,9 ****************************

In[128]:= Integrate[dxpsiL[x,z] dzfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[128]= -(-)
            2

**********************  For a_7,10 ****************************

In[129]:= Integrate[dxpsiR[x,z] dzfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[129]= -
          2

**********************  For a_7,11 ****************************

In[130]:= Integrate[dzpsiB[x,z] dzfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[130]= -(-)
            2

**********************  For a_7,12 ****************************

In[131]:= Integrate[dzpsiT[x,z] dzfiTR[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[131]= -
          2


**********************  For a_8,9 ****************************

In[132]:= Integrate[dxpsiL[x,z] dzfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[132]= -(-)
            2

**********************  For a_8,10 ****************************

In[133]:= Integrate[dxpsiR[x,z] dzfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[133]= -
          2

**********************  For a_8,11 ****************************

In[134]:= Integrate[dzpsiB[x,z] dzfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

            1
Out[134]= -(-)
            2

**********************  For a_8,12 ****************************


In[135]:= Integrate[dzpsiT[x,z] dzfiTL[x,z] , {x, 0, h}, {z, 0 , h}]

          1
Out[135]= -
          2

**********************  For a_99 ****************************

In[136]:= Integrate[dxpsiL[x,z] dxpsiL[x,z] , {x, 0, h}, {z, 0 , h}]

Out[136]= 1

**********************  For a_9,10 ****************************

In[137]:= Integrate[dxpsiR[x,z] dxpsiL[x,z] , {x, 0, h}, {z, 0 , h}]

Out[137]= -1

**********************  For a_9,11 ****************************

In[138]:= Integrate[dzpsiB[x,z] dxpsiL[x,z] , {x, 0, h}, {z, 0 , h}]

Out[138]= 1

**********************  For a_9,12 ****************************

In[139]:= Integrate[dzpsiT[x,z] dxpsiL[x,z] , {x, 0, h}, {z, 0 , h}]

Out[139]= -1

**********************  For a_10,10 ****************************

In[140]:= Integrate[dxpsiR[x,z] dxpsiR[x,z] , {x, 0, h}, {z, 0 , h}]

Out[140]= 1

**********************  For a_10,11 ****************************

In[141]:= Integrate[dzpsiB[x,z] dxpsiR[x,z] , {x, 0, h}, {z, 0 , h}]

Out[141]= -1

**********************  For a_10,12 ****************************

In[142]:= Integrate[dzpsiT[x,z] dxpsiR[x,z] , {x, 0, h}, {z, 0 , h}]

Out[142]= 1

**********************  For a_11,11 ****************************

In[143]:= Integrate[dzpsiB[x,z] dzpsiB[x,z] , {x, 0, h}, {z, 0 , h}]

Out[143]= 1

**********************  For a_11,12 ****************************

In[144]:= Integrate[dzpsiT[x,z] dzpsiB[x,z] , {x, 0, h}, {z, 0 , h}]

Out[144]= -1

**********************  For a_12,12 ****************************

In[145]:= Integrate[dzpsiT[x,z] dzpsiT[x,z] , {x, 0, h}, {z, 0 , h}]

Out[145]= 1