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int(0)^( pi)x sin x dx...

`int_(0)^( pi)x sin x dx`

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int_(0)^(pi) sin 3x dx

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int_(0)^(pi) x sin x cos^(2)x\ dx

int_(0)^(pi//2) x sin x cos x dx

(i) int_(0)^(pi//2) x sin x cos x dx (ii) int_(0)^(pi//6) (2+3x^(2)) cos 3x dx

Prove that : int_(0)^(pi) (x sin x)/(1+sinx) dx=pi((pi)/(2)-1)

If A= int _(0)^(pi) (sin x)/(x ^(2))dx, then int _(0)^(pi//2) (cos 2 x )/(x) dx is equal to: