# Question:Numerical Amounts of Definite Integrals

## Question:Numerical Amounts of Definite Integrals

#### Thanks

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restart:

Digits :=30: m := 4: g :=0.3: nu := 0.4: a := 1:k:=0.2:

W:=cos(n*2*evalf(Pi)*( r-k*a)/((1-k)*a)):

ODE:=((2*(diff(W, r, r, r, r))+2*(diff(W, r, r, r))/r-4*(diff(W, r, r))/r^2+4*(diff(W, r))/r^3-(2*(1-nu))*(diff(W, r, r, r))/r+(4*(1-nu))*(diff(W, r, r))/r^2-(4*(1-nu))*(diff(W, r))/r^3)*r*(1+g*r/a)^3+(2*(2*(diff(W, r, r, r))+2*(diff(W, r, r))/r-2*(diff(W, r))/r^2-(2*(1-nu))*(diff(W, r, r))/r+(2*(1-nu))*(diff(W, r))/r^2))*(1+g*r/a)^3+(6*(2*(diff(W, r, r, r))+2*(diff(W, r, r))/r-2*(diff(W, r))/r^2-(2*(1-nu))*(diff(W, r, r))/r+(2*(1-nu))*(diff(W, r))/r^2))*r*(1+g*r/a)^2*g/a+(6*(2*(diff(W, r, r))+2*(diff(W, r))/r-(2*(1-nu))*(diff(W, r))/r))*(1+g*r/a)^2*g/a+(6*(2*(diff(W, r, r))+2*(diff(W, r))/r-(2*(1-nu))*(diff(W, r))/r))*r*(1+g*r/a)*g^2/a^2-((2*(diff(W, r, r, r)+(diff(W, r, r))/r-(diff(W, r))/r^2))/r-(2*(diff(W, r, r)+(diff(W, r))/r))/r^2-(2*(1-nu))*(diff(W, r, r, r))/r+(2*(1-nu))*(diff(W, r, r))/r^2)*r*(1+g*r/a)^3-((2*(diff(W, r, r)+(diff(W, r))/r))/r-(2*(1-nu))*(diff(W, r, r))/r)*(1+g*r/a)^3-(3*((2*(diff(W, r, r)+(diff(W, r))/r))/r-(2*(1-nu))*(diff(W, r, r))/r))*r*(1+g*r/a)^2*g/a)/(2*(diff(W, r, r))*r+2*(diff(W, r))) :

for i from 1 to m do  for j from 1 to m do
C[i,j]:=int(subs(n=i,ODE)*subs(n=j,W),r=k*a..a)
end do:end do:

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