int sin^3 x cdot cos x , dx = | vedclass

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Question

(B) To solve the integral $\int \sin^3 x \cdot \cos x \, dx$,we use the method of substitution.Let $t = \sin x$.Then,differentiating both sides with r

Vedclass · Accepted Answer

$\frac{\sin^4 x}{4} + c$

Vedclass · Answer

(B) To solve the integral $\int \sin^3 x \cdot \cos x \, dx$,we use the method of substitution.Let $t = \sin x$.Then,differentiating both sides with respect to $x$,we get $dt = \cos x \, dx$.Substituting these into the integral,we have $\int t^3 \, dt$.The integral of $t^3$ with respect to $t$ is $\frac{t^4}{4} + c$.Substituting back $t = \sin x$,we get the final result $\frac{\sin^4 x}{4} + c$.

$\int \sin^3 x \cdot \cos x \, dx = $

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