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Question
Evaluate: `int_0^(pi/2) (sin2x)/(1 + sin^2x) "d"x`
Solution
`int_0^(pi/2) (sin2x)/(1 + sin^2x) "d"x = [log|1 + sin^2x|]_0^(pi/2)` .......`[∵ int ("f'"(x))/("f"(x)) "d"x = log|"f"(x)| + "c"]`
= `log |1 + sin^2(pi/2)| - log|1 + sin^2 0|`
= log |1 + 1| – log 1
= log 2 – 0
= log 2
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