Question

\( \int \left( \sin^{-1} x + \cos^{-1} x \right) dx\) = \(\underline{\hspace{2cm}}\)

Hint:

When dealing with inverse trigonometric functions, use known identities to simplify the expressions before integration.

Answer 1

Step 1: Using trigonometric identity.
We know that \( \sin^{-1} x + \cos^{-1} x = \frac{\pi}{2} \), so the integral becomes: \[ \int \left( \frac{\pi}{2} \right) dx = \frac{\pi}{2} x + C. \]

Step 2: Conclusion.
Thus, \( \int \left( \sin^{-1} x + \cos^{-1} x \right) dx = \frac{\pi}{2} x + C \).