Question

\(\int_0^1 \sin^{-1}x \, dx\) is

• A. \(\pi/2 -1\)
• B. 1
• C. \(\pi\)
• D. 0

Hint:

Inverse trig integrals → use integration by parts.

Answer 1

The Correct Option is A

Concept: Use integration by parts.

Step 1: Let
\[ u=\sin^{-1}x,\quad dv=dx \]

Step 2: Apply formula.
\[ \int u\,dv = uv - \int v\,du \] \[ = x\sin^{-1}x - \int \frac{x}{\sqrt{1-x^2}}dx \]

Step 3: Evaluate.
\[ = x\sin^{-1}x + \sqrt{1-x^2} \]

Step 4: Apply limits.
\[ = \left[\frac{\pi}{2} -1\right] \]