What is the integral from-2 to 1 of x(x+1)^2 ?

The integral from-2 to 1 of x(x+1)^2 is 3/4

integral from-2 to 1 of x(x+1)^2

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

\frac{3}{4}

Decimal

0.75

Solution steps

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

Expand

x (x + 1)^{2} : x^{3} + 2 x^{2} + x

= \int_{- 2}^{1} x^{3} + 2 x^{2} + 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_{- 2}^{1} x^{3} d x + \int_{- 2}^{1} 2 x^{2} d x + \int_{- 2}^{1} x d x

\int_{- 2}^{1} x^{3} d x = - \frac{15}{4}

\int_{- 2}^{1} 2 x^{2} d x = 6

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

= - \frac{15}{4} + 6 - \frac{3}{2}

Simplify

- \frac{15}{4} + 6 - \frac{3}{2} : \frac{3}{4}

= \frac{3}{4}

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What is the integral from-2 to 1 of x(x+1)^2 ?
The integral from-2 to 1 of x(x+1)^2 is 3/4