- sin-1-x- cos-1-xdx- xm-Find m

∫(sin^ 1√(x)+cos^ 1√(x))dx =∫(π2)dx =π2x Hence, m=2 ...

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Domain and Range of Basic Inverse Trigonometric Functions

∫ sin-1√x+ co...

Question

$\int ({sin}^{- 1} \sqrt{x} + {cos}^{- 1} \sqrt{x}) d x = \frac{π x}{m}$ .Find $m$

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Solution

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$\int \frac{s i n^{- 1} \sqrt{x} - c o s^{- 1} \sqrt{x}}{s i n^{- 1} \sqrt{x} + c o s^{- 1} \sqrt{x}} d x .$

I = \int c o s^{- 1} \sqrt{x} d x

J = \int \frac{s i n^{- 1} \sqrt{x} - c o s^{- 1} \sqrt{x}}{s i n^{- 1} \sqrt{x} + c o s^{- 1} \sqrt{x}} d x

A = \frac{1}{π} ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} {sin}^{- 1} (π x) & {tan}^{- 1} (\frac{π}{x}) {sin}^{- 1} (\frac{π}{x}) & {tan}^{- 1} (π x) \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦, B = \frac{1}{π} ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} - {cos}^{- 1} (π x) & {tan}^{- 1} (\frac{π}{x}) {sin}^{- 1} (\frac{π}{x}) & - {tan}^{- 1} (π x) \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

A - B

\int \frac{{sin}^{- 1} \sqrt{x} - {cos}^{- 1} \sqrt{x}}{{sin}^{- 1} \sqrt{x} + {cos}^{- 1} \sqrt{x}} d x

\int \frac{{sin}^{- 1} x - {cos}^{- 1} x}{{sin}^{- 1} x + {cos}^{- 1} x} d x

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