Mark M. answered 06/20/22
Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.
The graph of f(x) = √(25 - x2) is the upper half of the circle with center (0,0) and radius 5.
So, ∫(from 0 to 5) √(25 - x2) dx = area of half of the semicircle = (1/4)π(5)2 = 25π / 4