Question

Evaluate the definite integral x*(a^2-x^2)^(1/2) dx from 0 to a

(I'll repost this with the proper formatting)

Answer 1

\[\int\limits_{0}^{a} x \sqrt{a^2-x^2}dx\]

Answer 2

= -(1/3)(a^2-x^2)^(3/2) evaluated from 0 to a

= -(1/3)(0)^(3/2) - (-(1/3)(a^3)
=(1/3) * a^3