Multiple choice

What is the value of the definite integral $\int\limits_0^a \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a - x}}dx$?

  1. o

  2. a/2

  3. a

  4. 2a

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the property integral from 0 to a of f(x) dx = integral from 0 to a of f(a-x) dx, let I be the integral. Then I = integral from 0 to a of sqrt(a-x)/(sqrt(a-x) + sqrt(x)) dx. Adding the two expressions for I gives 2I = integral from 0 to a of 1 dx = a, so I = a/2.