int sin^2 x cos x , dx is equal to | vedclass

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(C) Let $I = \int \sin^2 x \cos x \, dx$. Substitute $\sin x = t$. Differentiating both sides with respect to $x$,we get $\cos x \, dx = dt$. Substitu

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$\frac{\sin^3 x}{3} + c$

Vedclass · Answer

(C) Let $I = \int \sin^2 x \cos x \, dx$. Substitute $\sin x = t$. Differentiating both sides with respect to $x$,we get $\cos x \, dx = dt$. Substituting these into the integral,we get $I = \int t^2 \, dt$. Integrating $t^2$ with respect to $t$,we get $I = \frac{t^3}{3} + c$. Substituting back $t = \sin x$,we get $I = \frac{\sin^3 x}{3} + c$.

$\int \sin^2 x \cos x \, dx$ is equal to

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