Q. Primitive of $\cos^{- 1}x\ w.r.t\ x\ is$
A) $x\cos^{- 1}{x - \frac{1}{2}\sqrt{1 - x^{2}} + c}$
B) $x\cos^{- 1}{x - \sqrt{1 - x^{2}} + c}$
C) $x\cos^{- 1}{x + \sqrt{1 - x^{2}} + c}$
D) $x\cos^{- 1}{+ \frac{1}{2}\sqrt{1 - x^{2}} + c}$
Explanation
(b)
$\int_{}^{}{1\cos^{- 1}x}\ dx = x\cos^{- 1}x + \int_{}^{}x.\ \frac{1}{\sqrt{1 - x^{2}}}\ dx$
$= x\cos^{- 1}x - \frac{1}{2}\ \int_{}^{}\frac{( - 2x)}{\sqrt{1 - x^{2}}}\ dx$
$= x\cos^{- 1}{x - \sqrt{1 - x^{2}} + c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.