Integrate the function: frac{cos x}{sqrt{4-si | vedclass

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(B) To integrate the function $\int \frac{\cos x}{\sqrt{4-\sin ^{2} x}} dx$,we use the method of substitution.Let $\sin x = t$.Then,differentiating bo

Vedclass · Accepted Answer

$\sin ^{-1}(\frac{\sin x}{2})+C$

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(B) To integrate the function $\int \frac{\cos x}{\sqrt{4-\sin ^{2} x}} dx$,we use the method of substitution.Let $\sin x = t$.Then,differentiating both sides with respect to $x$,we get $\cos x dx = dt$.Substituting these into the integral,we have:$\int \frac{dt}{\sqrt{2^2 - t^2}}$.Using the standard integration formula $\int \frac{1}{\sqrt{a^2 - x^2}} dx = \sin^{-1}(\frac{x}{a}) + C$,where $a = 2$ and $x = t$,we get:$\sin^{-1}(\frac{t}{2}) + C$.Substituting back $t = \sin x$,the final result is:$\sin^{-1}(\frac{\sin x}{2}) + C$.

Integrate the function: $\frac{\cos x}{\sqrt{4-\sin ^{2} x}}$

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