Question

Let \[ \int \frac{x^{1/2}}{\sqrt{1 - x^3}} \, dx = \frac{3}{3} \, g(x) + C \] then

• A. \( f(x) = \sqrt{x} \)
• B. \( f(x) = x^3 \)
• C. \( g(x) = \sin^{-1} x \)
• D. None of these

Hint:

The inverse sine function can appear when integrating functions involving square roots and cubes.

Answer 1

The Correct Option is B

The integral can be simplified and \( g(x) \) turns out to be the inverse sine function \( \sin^{-1} x \).