Prove
Question:

$\int(1-x) \sqrt{x} d x$

Solution:

$\int(1-x) \sqrt{x} d x$

$=\int\left(\sqrt{x}-x^{\frac{3}{2}}\right) d x$

$=\int x^{\frac{1}{2}} d x-\int x^{\frac{3}{2}} d x$

$=\frac{x^{\frac{3}{2}}}{\frac{3}{2}}-\frac{x^{\frac{5}{2}}}{\frac{5}{2}}+\mathrm{C}$

$=\frac{2}{3} x^{\frac{3}{2}}-\frac{2}{5} x^{\frac{5}{2}}+\mathrm{C}$

Administrator

Leave a comment

Please enter comment.
Please enter your name.