Question

The value of the integral
\[ \int_a^b \frac{\sqrt{x} \, dx}{\sqrt{x} + \sqrt{a + b - x}} \]
is:

• A. \(\pi\)
• B. \(\dfrac{1}{2}(b-a)\)
• C. \(\dfrac{\pi}{2}\)
• D. b-a

Hint:

Use symmetry property: \[ I = \int_a^b f(x) \, dx = \int_a^b f(a+b-x) \, dx \]

Answer 1

The Correct Option is B