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Evaluate ππ∫-π2π2sinx1+cos2xdx -

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Question

Evaluate `int_(-π/2)^(π/2) sinx/(1 + cos^2x)dx`

Sum

Solution

Here f(x) = `sinx/(1 + cos^2x)` is an odd function

∴ `int_(-π/2)^(π/2) sinx/(1 + cos^2x)dx` = 0  ...(Theorem)

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Methods of Evaluation and Properties of Definite Integral
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