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int(0)^(pi)(x tanx)/((secxcosecx))dx=(pi...

`int_(0)^(pi)(x tanx)/((secxcosecx))dx=(pi^(2))/(4)`

Text Solution

Verified by Experts

`I=int_(0)^(pi)xsin^(2)xdx` and `I=int_(0)^(pi)(pi-x)sin^(2)(pi-x)dx=int_(0)^(pi)(pi-x)sin^(2)xdx`.
`:.2I=pi*int_(0)^(pi)sin^(2)xdx=(pi)/(2)*int_(0)^(pi)/(2)(1-cos2x)dx`.
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