Integrate the function sin x cdot sin (cos x) | vedclass

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Question

(A) Let $I = \int \sin x \cdot \sin (\cos x) \, dx$. Substitute $\cos x = t$. Differentiating both sides with respect to $x$,we get $-\sin x \, dx = d

Vedclass · Accepted Answer

$\cos (\cos x) + C$

Vedclass · Answer

(A) Let $I = \int \sin x \cdot \sin (\cos x) \, dx$. Substitute $\cos x = t$. Differentiating both sides with respect to $x$,we get $-\sin x \, dx = dt$,or $\sin x \, dx = -dt$. Substituting these into the integral,we get: $I = \int \sin (t) \cdot (-dt) = -\int \sin t \, dt$. The integral of $\sin t$ is $-\cos t$. Therefore,$I = -(-\cos t) + C = \cos t + C$. Substituting back $t = \cos x$,we get the final result: $I = \cos (\cos x) + C$,where $C$ is an arbitrary constant.

Integrate the function $\sin x \cdot \sin (\cos x)$.

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