int sqrt{1+cos x} , dx is equal to | vedclass

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(B) We know that $1 + \cos x = 2 \cos^2 \left(\frac{x}{2}\right)$.Substituting this into the integral,we get:$\int \sqrt{2 \cos^2 \left(\frac{x}{2}\ri

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$2 \sqrt{2} \sin \frac{x}{2} + C$

Vedclass · Answer

(B) We know that $1 + \cos x = 2 \cos^2 \left(\frac{x}{2}\right)$.Substituting this into the integral,we get:$\int \sqrt{2 \cos^2 \left(\frac{x}{2}\right)} \, dx = \int \sqrt{2} \left| \cos \left(\frac{x}{2}\right) \right| \, dx$.Assuming $\cos \left(\frac{x}{2}\right) > 0$,we have:$\sqrt{2} \int \cos \left(\frac{x}{2}\right) \, dx$.Integrating with respect to $x$:$\sqrt{2} \cdot \frac{\sin \left(\frac{x}{2}\right)}{1/2} + C = 2 \sqrt{2} \sin \left(\frac{x}{2}\right) + C$.

$\int \sqrt{1+\cos x} \, dx$ is equal to

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