The value of int_{-1 / 2}^{1 / 2} cos ^{-1} x | vedclass

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(B) We have,$I = \int_{-1 / 2}^{1 / 2} \cos ^{-1} x \, dx$. Using the property $\cos^{-1} x = \frac{\pi}{2} - \sin^{-1} x$,we get: $I = \int_{-1 / 2}^

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$\frac{\pi}{2}$

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(B) We have,$I = \int_{-1 / 2}^{1 / 2} \cos ^{-1} x \, dx$. Using the property $\cos^{-1} x = \frac{\pi}{2} - \sin^{-1} x$,we get: $I = \int_{-1 / 2}^{1 / 2} (\frac{\pi}{2} - \sin^{-1} x) \, dx$. $I = \int_{-1 / 2}^{1 / 2} \frac{\pi}{2} \, dx - \int_{-1 / 2}^{1 / 2} \sin^{-1} x \, dx$. Since $\sin^{-1} x$ is an odd function,the integral $\int_{-a}^{a} \sin^{-1} x \, dx = 0$. Therefore,$I = \frac{\pi}{2} [x]_{-1 / 2}^{1 / 2} - 0$. $I = \frac{\pi}{2} (\frac{1}{2} - (- \frac{1}{2})) = \frac{\pi}{2} (1) = \frac{\pi}{2}$.

The value of $\int_{-1 / 2}^{1 / 2} \cos ^{-1} x \, dx$ is

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