int (sin^{-1} x + cos^{-1} x) , dx = | vedclass

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(C) We know that for $x \in [-1, 1]$,the identity $\sin^{-1} x + \cos^{-1} x = \frac{\pi}{2}$ holds true.Substituting this into the integral,we get:$\

Vedclass · Accepted Answer

Both $(a)$ and $(b)$

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(C) We know that for $x \in [-1, 1]$,the identity $\sin^{-1} x + \cos^{-1} x = \frac{\pi}{2}$ holds true.Substituting this into the integral,we get:$\int (\sin^{-1} x + \cos^{-1} x) \, dx = \int \frac{\pi}{2} \, dx = \frac{\pi x}{2} + c$.This matches option $(a)$.Now,consider option $(b)$: $x(\cos^{-1} x + \sin^{-1} x) + c = x(\frac{\pi}{2}) + c = \frac{\pi x}{2} + c$.Since both expressions simplify to the same result,both $(a)$ and $(b)$ are correct.

$\int (\sin^{-1} x + \cos^{-1} x) \, dx = $

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