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

The integral from 0 to 2 of x(x-2)^2 is 4/3

Popular >

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

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

\frac{4}{3}

Decimal Notation

1.33333 \dots

Solution steps

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

Expand

x (x - 2)^{2} : x^{3} - 4 x^{2} + 4 x

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

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

\int_{0}^{2} 4 x^{2} d x = \frac{32}{3}

\int_{0}^{2} 4 x d x = 8

= 4 - \frac{32}{3} + 8

Simplify

4 - \frac{32}{3} + 8 : \frac{4}{3}

= \frac{4}{3}

\int_{1}^{2} \frac{1}{x ^{3} + 8} d x

\int_{1}^{e} \frac{5}{x} d x

\int_{0}^{1} (x e^{x}) d x

\int_{0}^{3} 4 - 4 x + x^{2} d x

\int_{1}^{4} ∣ 3 x - 6 ∣ d x

What is the integral from 0 to 2 of x(x-2)^2 ?
The integral from 0 to 2 of x(x-2)^2 is 4/3