What is the integral from 0 to 2 of x^2(sqrt(2x)-x) ?

The integral from 0 to 2 of x^2(sqrt(2x)-x) is 4/7

Popular >

integral from 0 to 2 of x^2(sqrt(2x)-x)

\int_{0}^{2} x^{2} (2 x - x) d x

\frac{4}{7}

Decimal

0.57142 \dots

Solution steps

\int_{0}^{2} x^{2} (2 x - x) d x

Expand

x^{2} (2 x - x) : 2 x^{\frac{5}{2}} - x^{3}

= \int_{0}^{2} 2 x^{\frac{5}{2}} - x^{3} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{2} 2 x^{\frac{5}{2}} d x - \int_{0}^{2} x^{3} d x

\int_{0}^{2} 2 x^{\frac{5}{2}} d x = \frac{32}{7}

\int_{0}^{2} x^{3} d x = 4

= \frac{32}{7} - 4

Simplify

\frac{32}{7} - 4 : \frac{4}{7}

= \frac{4}{7}

\int_{0}^{1} (x^{2} + 6) d x

\int_{- 5 π}^{6 π} cos^{2} (x) d x

\int_{0}^{2} - x^{2} + 4 d x

\int_{0}^{7} 3 x + 9 d x

\int_{- 2}^{14} ln (t) sin (t) d t

What is the integral from 0 to 2 of x^2(sqrt(2x)-x) ?
The integral from 0 to 2 of x^2(sqrt(2x)-x) is 4/7