Question

Evaluate: \[ \int \sin^{-1}x\,dx-\int \cos^{-1}x\,dx. \]

• A. x(\sin^{-1}x-\cos^{-1}x)-2\sqrt{1-x^2}+C
• B. x(2\sin^{-1}x+\frac{\pi}{2})-2\sqrt{1-x^2}+C
• C. x(\sin^{-1}x-\cos^{-1}x)+2\sqrt{1-x^2}+C
• D. x(\frac{\pi}{2}+\cos^{-1}x)+2\sqrt{1-x^2}+C

Hint:

Always remember: \[ \sin^{-1}x+\cos^{-1}x=\frac{\pi}{2}. \] It simplifies many inverse trigonometric integrals immediately.

Answer 1

The Correct Option is B