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[?] Integrate a given symbolic limit of integration?

Aidan Droogan
Posted 7 years ago

Hi, I am new to Mathematica. Please advise how I can obtain the symbolic result of the following integral, where n is a positive integer and a is a real number. Thank you.

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POSTED BY: Aidan Droogan
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Aidan Droogan
Aidan Droogan
Posted 7 years ago
POSTED BY: Aidan Droogan
POSTED BY: Daniel Lichtblau

With correct syntax:

In[2]:= Integrate[(2 x^2/a) Sin[n Pi x/a]^2, {x, 0, a}]

Out[2]= (a^2 (4 n^3 \[Pi]^3 - 
   6 n \[Pi] Cos[2 n \[Pi]] + (3 - 6 n^2 \[Pi]^2) Sin[
     2 n \[Pi]]))/(12 n^3 \[Pi]^3)
POSTED BY: S M Blinder

You can use Simplify:

Simplify[Integrate[(2 x^2)/a Sin[n*Pi*x/a]^2, {x, 0, a}], 
 Element[n, Integers]]

or Assuming:

Assuming[Element[n, Integers], 
 Integrate[(2 x^2)/a Sin[n*Pi*x/a]^2, {x, 0, a}]]

Assumptions inside Integrate has no particular effect:

Integrate[(2 x^2)/a Sin[n*Pi*x/a]^2, {x, 0, a}, 
 Assumptions -> Element[n, Integers]]
POSTED BY: Gianluca Gorni
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