What is the integral from-2 to 0 of x^3+x^2-2x ?

The integral from-2 to 0 of x^3+x^2-2x is 8/3

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integral from-2 to 0 of x^3+x^2-2x

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

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

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

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

\int_{- 2}^{0} x^{2} d x = \frac{8}{3}

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

= - 4 + \frac{8}{3} - (- 4)

Simplify

= \frac{8}{3}

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\int_{0}^{1} 12 x ln (3 x) d x

\int_{0}^{2} 16 - 2 x d x

What is the integral from-2 to 0 of x^3+x^2-2x ?
The integral from-2 to 0 of x^3+x^2-2x is 8/3