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मान ज्ञात कीजिए : int(0)^(pi)(x sin x )...

मान ज्ञात कीजिए `:` `int_(0)^(pi)(x sin x )/(1+ cos^(2)x)dx`

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int_(0)^( pi)(sin x)/(1+cos^(2)x)dx =

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

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

int_(0)^( pi/2)(sin x)/(1+cos x)dx

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

int_(0)^(pi//2)(sin x.cos x)/(1+sin^(4)x)dx=

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

int_(0)^(pi//2)(sin x - cos x)/(1-sin x cos x)dx=

int_(0)^(pi//2)(1+sin x)/(2+sin x + cos x) dx=

int_(0)^((pi)/(2))(sin x cos x)/(1+sin^(4)x)dx