The correct option is B π/2∫_0^π f(sin x)dx∫_0^πx f (sin x)dx = π/2∫_0^π f(sin x)dx Since ∫_0^π xf (x)dx =1/2a ∫_0^πf(x)dx, if f(a x)=f(x) ...

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Integration of Piecewise Continuous Functions

∫0πx f sin xd...

Question

$\int_{0}^{π} x f (s i n x) d x =$

π \int_{0}^{π} f (s i n x) d x

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\frac{π}{2} \int_{0}^{π} f (s i n x) d x

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\frac{π}{2} \int_{0}^{\frac{π}{2}} f (s i n x) d x

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Solution

The correct option is B $\frac{π}{2} \int_{0}^{π} f (s i n x) d x$
$\int_{0}^{π} x f (s i n x) d x = \frac{π}{2} \int_{0}^{π} f (s i n x) d x$
$S i n c e \int_{0}^{π} x f (x) d x = \frac{1}{2} a \int_{0}^{π} f (x) d x, i f f (a - x) = f (x)$

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