Integration question, answer is given
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Integration question, answer is given

[From: ] [author: ] [Date: 11-09-25] [Hit: ]
......
∫ (b,0) a²sin²(πx/b) / 2

where b = upper limit
where 0 = lower limit

answer is a²b/4

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The a^2/2 is just a constant and can be pulled out of the integral

a²/2 ∫ (b,0) sin²(πx/b)

Use the half angle formula

a²/2 ∫ (b,0) [1-Cos(2πx/b)]/2

Pull out the extra 1/2 u picked up when u used the half angle formula

a²/4 ∫ (b,0) [1-Cos(2πx/b)]

Now the integral is easy

a²/4 [(b - b/2π Sin(2π)) - (0-b/2π Sin(0))] = a²b/4
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