Mathematics

solve it.
$$I = \int {{x^2}\cos x} dx$$


SOLUTION
$$I=\displaystyle\int{{x}^{2}\cos{x}dx}$$
Let $$u={x}^{2}\Rightarrow\,du=2x\,dx$$
$$dv=\cos{x}dx\Rightarrow\,v=\sin{x}$$
$$I={x}^{2}\sin{x}-\displaystyle\int{2x\sin{x}\,dx}$$
$$I={x}^{2}\sin{x}-2\displaystyle\int{x\sin{x}\,dx}$$
Let $$u=x\Rightarrow\,du=dx$$
$$dv=\sin{x}dx\Rightarrow\,v=-\cos{x}$$
$$I={x}^{2}\sin{x}-2\left[-x\cos{x}+\displaystyle\int{\cos{x}dx}\right]$$
$$I={x}^{2}\sin{x}+2x\cos{x}-2\displaystyle\int{\cos{x}dx}$$
$$I={x}^{2}\sin{x}+2x\cos{x}-2\sin{x}+c$$

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Subjective Medium Published on 17th 09, 2020
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