Question

Evaluate \( \int_{1/n}^{(n-1)/n} \frac{\sqrt{x}}{\sqrt{a-x} + \sqrt{x}} \, dx \).

• A. \( \frac{a}{2} \)
• B. \( \frac{n\cdot a + 2}{2n} \)
• C. \( \frac{n\cdot a - 2}{2n} \)
• D. \( \frac{n\cdot a}{2} \)

Hint:

For expressions of the form \( f(x) \) and \( f(a-x) \), try adding them to simplify the integral to a constant.

Answer 1

The Correct Option is C