Question

Integration from 0 to 1

Answer 1

$\int\limits^1_0 {x \sqrt{1-x^2}} \, dx = \int\limits^1_0 {x(1-x^2)^{ \frac{1}{2}}} \, dx$
$[\frac{\frac{2}{3} x(1-x^2)^{ \frac{3}{2}}}{-2x}]^1_0$
$[- \frac{1}{3}(1-x^2)^{ \frac{3}{2} }]^1_0$
$0-- \frac{1}{3} = \frac{1}{3}$