Question

how do I find the integral of sqrt(16x - x^2)?

Answer 1

Not sure I could do it by hand anymore, but in a book of integrals, we find INT(SQRT(2ax-x^2)dx. That's your integral, with a=8.

The answer is quite lengthy; too long for me to type. Worst case, get it from integrals.com or wolframalpha.com.

Answer 2

Like LBickford the answer is kind of complicated but here are the steps.
(1) Complete the square inside the square root--SQRT(64- (x-8)^2)
(2) Use u substitution-- u=x-8
(3) Use z substitution-- z = \[\sin \theta\]