Prove: ∫ From 0 to pi x f(sinx) dx = pi/2 ∫ From 0 to pi f(sinx) dx - Integration by Substitution

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SL NO 417. Integration . x f ( sinx) dx. range 0 to 180⁰ . Class 12 above. SL NO 417. Integration . x f ( sinx) dx. range 0 to 180⁰ . Class 12 above.
The integral `int_(0)^(pi) x f(sinx )dx` is equal to The integral `int_(0)^(pi) x f(sinx )dx` is equal to
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(i) Show that `int_(0)^(pi)xf(sinx)dx =(pi)/(2)int_(0)^(pi)f (sin x)dx. (i) Show that `int_(0)^(pi)xf(sinx)dx =(pi)/(2)int_(0)^(pi)f (sin x)dx.
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If `int_(0)^(pi)xf(sinx)dx=A int_(0)^(pi//2) f(sinx)dx`, then A is If `int_(0)^(pi)xf(sinx)dx=A int_(0)^(pi//2) f(sinx)dx`, then A is
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Show that, int_(0)^(pi)xf(sinx)dx=(pi)/(2)int_(0)^(pi)f(sinx)dx. | 12 | DEFINITE INTEGRAL | MAT... Show that, int_(0)^(pi)xf(sinx)dx=(pi)/(2)int_(0)^(pi)f(sinx)dx. | 12 | DEFINITE INTEGRAL | MAT...