What is the integral from-1 to 0 of x^2(x-2) ?

The integral from-1 to 0 of x^2(x-2) is -11/12

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integral from-1 to 0 of x^2(x-2)

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

- \frac{11}{12}

Decimal Notation

- 0.91666 \dots

Solution steps

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

Expand

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

= \int_{- 1}^{0} x^{3} - 2 x^{2} 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_{- 1}^{0} x^{3} d x - \int_{- 1}^{0} 2 x^{2} d x

\int_{- 1}^{0} x^{3} d x = - \frac{1}{4}

\int_{- 1}^{0} 2 x^{2} d x = \frac{2}{3}

= - \frac{1}{4} - \frac{2}{3}

Simplify

- \frac{1}{4} - \frac{2}{3} : - \frac{11}{12}

= - \frac{11}{12}

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\int_{1}^{2} 18 x + 37 d x

What is the integral from-1 to 0 of x^2(x-2) ?
The integral from-1 to 0 of x^2(x-2) is -11/12