mimi990

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1 years, 171 days

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These are questions asked by mimi990

 

Good morning everyone, 

I have a problem, when I try to evaluate the definite integral below, Maple can not provide a result. What can I do so that the Maple can calculate this integral?

This is the Maple code with the result:

 

 

restart

with(VectorCalculus):

with(LinearAlgebra):

with(CodeGeneration):

N := 1:

M := 2:

``

for i to N do rpv1 || i := 0; rpv2 || i := 0; rpv3 || i := 0; for j to M do rpv1 || i := VectorCalculus:-`+`(rpv1 || i, Typesetting:-delayDotProduct(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), Phi || i || j)); rpv2 || i := VectorCalculus:-`+`(rpv2 || i, Typesetting:-delayDotProduct(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), `ϕ` || i || j)); rpv3 || i := VectorCalculus:-`+`(rpv3 || i, Typesetting:-delayDotProduct(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), gamma || i || j)) end do; rp || i := Matrix([[rpv1 || i], [rpv2 || i], [rpv3 || i]]) end do:

``

for i to N do rppv1 || i := 0; rppv2 || i := 0; rppv3 || i := 0; for j to M do rppv1 || i := VectorCalculus:-`+`(rppv1 || i, Typesetting:-delayDotProduct(diff(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), s), Phi || i || j)); rppv2 || i := VectorCalculus:-`+`(rppv2 || i, Typesetting:-delayDotProduct(diff(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), s), `ϕ` || i || j)); rppv3 || i := VectorCalculus:-`+`(rppv3 || i, Typesetting:-delayDotProduct(diff(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), s), gamma || i || j)) end do; rpp || i := Matrix([[rppv1 || i], [rppv2 || i], [rppv3 || i]]) end do:

``

``

for i to N do for j from 0 to 0 do U || i || j := 0 end do end do:

for i to N do for j from 0 to 0 do V || i || j := 0 end do end do:

for i to N do for j from 0 to 0 do W || i || j := 0 end do end do:

for i to N do for j from 0 to VectorCalculus:-`+`(M, -2) do U || i || (VectorCalculus:-`+`(j, 1)) := VectorCalculus:-`+`(U || i || j, VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^VectorCalculus:-`+`(j, 1)) end do end do:

for i to N do for j from 0 to VectorCalculus:-`+`(M, -2) do V || i || (VectorCalculus:-`+`(j, 1)) := VectorCalculus:-`+`(V || i || j, VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^VectorCalculus:-`+`(j, 1)) end do end do:

for i to N do for j from 0 to VectorCalculus:-`+`(M, -2) do W || i || (VectorCalculus:-`+`(j, 1)) := VectorCalculus:-`+`(W || i || j, VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^VectorCalculus:-`+`(j, 1)) end do end do:

for i to N do f || i := VectorCalculus:-`+`(Typesetting:-delayDotProduct(VectorCalculus:-`*`(Typesetting:-delayDotProduct(E, A), 1/mu), VectorCalculus:-`+`(VectorCalculus:-`+`(rpp || i, VectorCalculus:-`-`(VectorCalculus:-`*`(rpp || i, 1/evalc(norm(Re(rp || i), 2))))), VectorCalculus:-`*`(Typesetting:-delayDotProduct(rp || i, Typesetting:-delayDotProduct(rp || i^%T, rpp || i)), 1/evalc(norm(Re(rp || i), 2))^3))), Typesetting:-delayDotProduct(g, e3)) end do:

for i to N do for j to VectorCalculus:-`+`(M, -1) do fun || i || j := int(VectorCalculus:-`*`(U || i || j, Row(f || i, 1)), s = xi || i .. L || i) end do end do;

fun11

(int((s-xi1)*(E*A*(2*Phi12/L1^2-2*Phi12/(sqrt((gamma11/L1+2*gamma12*s/L1^2-2*gamma12*xi1/L1^2)^2+(`ϕ11`/L1+2*`ϕ12`*s/L1^2-2*`ϕ12`*xi1/L1^2)^2+(Phi11/L1+2*Phi12*s/L1^2-2*Phi12*xi1/L1^2)^2)*L1^2)+(Phi11/L1+(2*(s-xi1))*Phi12/L1^2)*((2*(Phi11/L1+(2*(s-xi1))*Phi12/L1^2))*Phi12/L1^2+(2*(`ϕ11`/L1+(2*(s-xi1))*`ϕ12`/L1^2))*`ϕ12`/L1^2+(2*(gamma11/L1+(2*(s-xi1))*gamma12/L1^2))*gamma12/L1^2)/((gamma11/L1+2*gamma12*s/L1^2-2*gamma12*xi1/L1^2)^2+(`ϕ11`/L1+2*`ϕ12`*s/L1^2-2*`ϕ12`*xi1/L1^2)^2+(Phi11/L1+2*Phi12*s/L1^2-2*Phi12*xi1/L1^2)^2)^(3/2))/mu+g*e3)/L1, s = xi1 .. L1))*e[x]

(1.1)

``

NULL

``


 

Download integral.mw

 

Thank you !

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