Originally Posted by

**tom@ballooncalculus** You're thinking product rule, which if you were really thorough about it would give become integration by parts... but far easier here is to multiply out the brackets in (1/2) ∫(0 to 1) (u-1) * sqrt(u) du and then apply the power rule, which you seem to know. Don't forget to re-set the limits for u, also. Indeed, then there's no need to convert back to t - you can evaluate the integral directly.

$\displaystyle \int_1^2 (u-1) u^{\frac{1}{2}}\ du = \int_1^2 (u^{\frac{3}{2}} - u^{\frac{1}{2}})\ du = ...$