The value of ∫x−3sin−1⁡loge⁡x+cos−1⁡loge⁡xdx is

x−3 is defined whenx≥3sin−1⁡loge⁡x is defined when −1≤loge⁡x≤1⇒1e≤x≤e⇒ no value of 'x' will satisfy both

The value of ∫x−3sin−1⁡loge⁡x+cos−1⁡loge⁡xdx is

x−3 is defined whenx≥3sin−1⁡loge⁡x is defined when −1≤loge⁡x≤1⇒1e≤x≤e⇒ no value of 'x' will satisfy both

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The value of $\int \sqrt{x - 3} \{\sin^{- 1} (\log_{e} x) + \cos^{- 1} (\log_{e} x)\} dx$ is

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is equal to $\frac{π}{3} (x - 3)^{3 / 2}$

$\frac{π}{3} (x)^{3 / 2}$

$\frac{π}{2} (x - 3)^{3 / 2}$

Does not exist

answer is D.

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Detailed Solution

$\sqrt{x - 3}$ is defined when $x \geq 3 \sin^{- 1} (\log_{e} x)$ is defined when $- 1 \leq \log_{e} x \leq 1 \Rightarrow \frac{1}{e} \leq x \leq e \Rightarrow$ no value of 'x' will satisfy both

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The value of ∫x−3sin−1⁡loge⁡x+cos−1⁡loge⁡xdx is

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The value of $\int \sqrt{x - 3} \{\sin^{- 1} (\log_{e} x) + \cos^{- 1} (\log_{e} x)\} dx$ is