Question

The value of the integral \[ \int_{3}^{6} \frac{\sqrt{x}}{\sqrt{9 - x} + \sqrt{x}} \, dx \] is:

• A. \( \frac{1}{2} \)
• B. \( \frac{3}{2} \)
• C. \( 2 \)
• D. \( 1 \)

Hint:

For symmetric integrals: Use \( x \to a+b-x \) substitution. Adding the transformed integral often simplifies radicals.

Answer 1

The Correct Option is C