The value of the definite integral ∫₂⁸ [√(10 − x)/(√x + √(10 − x))] dx is:
A
13
B
6
C
10
D
3
Correct Option:
D
Explanation
Let I = ∫₂⁸ [√(10 − x)/(√x + √(10 − x))] dx and f(x) = √(10 − x)/(√x + √(10 − x)). Then f(10 − x) = 1 − f(x). Because the interval [2, 8] is symmetric under x → 10 − x, 2I = ∫₂⁸ 1 dx = 6, so I = 3.
