Q. $\int_{}^{}{\cos{\left\lbrack 2\cot^{- 1}\sqrt{\frac{1 - x}{1 + x}} \right\rbrack\ dx}}$ is equal to
A) $\frac{1}{2}x^{2} + c$
B) $\frac{1}{2}\sin{\left\lbrack 2\cot^{- 1}\sqrt{\frac{1 - x}{1 + x}} \right\rbrack + c}$
C) $- \frac{1}{2}x^{2} + c$
D) $\frac{1}{2}x + c$
Explanation
(c)
$\int_{}^{}{\cos{\left\lbrack 2\cot^{- 1}\sqrt{\frac{1 - x}{1 + x}} \right\rbrack\ dx}}$
$= \int_{}^{}{\cos{\lbrack\cos^{- 1}{( - x)\rbrack dx}}}$
$= \int_{}^{}{( - x)dx = - \frac{x^{2}}{2} + c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.