Question

Evaluate:
$\int (1-x)\sqrt{x}dx$

Answer 1

We have,

$I=\int (1-x)\sqrt{x}dx$

$I=\int (\sqrt{x}-x\sqrt{x})dx$

$I=\int \left(\right(x{)}^{\frac{1}{2}}-\left(x{)}^{\frac{3}{2}}\right)dx$

$I=\frac{(x{)}^{\frac{3}{2}}}{\frac{3}{2}}-\frac{(x{)}^{\frac{5}{2}}}{\frac{5}{2}}+C$

$I=\frac{2(x{)}^{\frac{3}{2}}}{3}-\frac{2(x{)}^{\frac{5}{2}}}{5}+C$

Hence, this is the answer.