Mathematics


$$\displaystyle \int_{0}^{\pi}x.\sin^{3}xdx_{=}$$


ANSWER

$$\displaystyle \frac{2\pi}{3}$$


SOLUTION
$$I=\int_{0}^{\pi}x\ sin^{3}x\ dx$$
$$I=\int_{0}^{\pi}(\pi-x) sin^{3}x\ dx$$
$$I=\pi \int_{0}^{\pi}x\ sin^{3}x\ dx=I$$
$$2I=2\pi \left ( \dfrac{2}{3} \right )$$
$$I=2 {\pi}/{3}$$
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Single Correct Medium Published on 17th 09, 2020
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