Question

\[\int\limits_0^{\pi/2} x \sin x\ dx\]  is equal to

पर्याय

•  π/4

•  π/2

• π

• 1

Answer 1

1

\[\text{We have}, \]

\[ I = \int_0^\frac{\pi}{2} x \sin x\ d x \]

\[ = \left[ - x \cos x \right]_0^\frac{\pi}{2} - \int_0^\frac{\pi}{2} 1\left( - \cos x \right) d x\]

\[ = \left[ - x \cos x \right]_0^\frac{\pi}{2} + \int_0^\frac{\pi}{2} \cos x\ d x\]

\[ = - \left[ x \cos x \right]_0^\frac{\pi}{2} + \left[ \sin x \right]_0^\frac{\pi}{2} \]

\[ = - \left[ 0 - 0 \right] + \left[ 1 - 0 \right]\]

\[ = 1\]