What is the integral from-2 to 1 of x^3+x^2-2x ?

The integral from-2 to 1 of x^3+x^2-2x is 9/4

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integral from-2 to 1 of x^3+x^2-2x

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

\frac{9}{4}

Decimal

2.25

Solution steps

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

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

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

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

= - \frac{15}{4} + 3 - (- 3)

Simplify

- \frac{15}{4} + 3 - (- 3) : \frac{9}{4}

= \frac{9}{4}

What is the integral from-2 to 1 of x^3+x^2-2x ?
The integral from-2 to 1 of x^3+x^2-2x is 9/4