The value of $\int_{0}^{\frac{3\pi}{2}}\frac{| an^{- 1}{ an{x|}} - |\sin^{- 1}{\sin{x|}}}{\left| an^{- 1}{ an x} ight| + {|\sin^{- 1}}{\sin x|}}dx$ is equal to

Question

The value of $\int_{0}^{\frac{3\pi}{2}}\frac{|	an^{- 1}{	an{x|}} - |\sin^{- 1}{\sin{x|}}}{\left| 	an^{- 1}{	an x} ight| + {|\sin^{- 1}}{\sin x|}}dx$ is equal to

Dr. Abubacker · Accepted Answer

(d)
$\because\$Integrand is discontinuous at $\frac{\pi}{2}$, then
$\int_{0}^{\pi/2}{0.dx + \int_{\pi/2}^{3\pi/2}{0.dx = 0}}$
$\because\ 0 < x < \frac{\pi}{2},\ |	an^{- 1}{	an{x| = |\sin^{- 1}{\sin{x|}}}}$
and $\frac{\pi}{2} < x < \frac{3\pi}{2},\ |	an^{- 1}{	an{x| = |\sin^{- 1}{\sin{x|}}}}$

Q. The value of $\int_{0}^{\frac{3\pi}{2}}\frac{|\tan^{- 1}{\tan{x|}} - |\sin^{- 1}{\sin{x|}}}{\left| \tan^{- 1}{\tan x} \right| + {|\sin^{- 1}}{\sin x|}}dx$ is equal to

Explanation

Reviewed by Dr. Abubacker

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