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

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

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integral from 0 to-2 of x^2

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

- \frac{8}{3}

Decimal

- 2.66666 \dots

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{- 2}^{0}

= - [\frac{x ^{3}}{3}]_{- 2}^{0}

Compute the boundaries:

\frac{8}{3}

= - \frac{8}{3}

\int_{1}^{4} (x - 3) d x

\int_{1}^{2} x^{2} (x^{3} + 5)^{4} d x

\int_{0}^{1} sin (t) cos (t) d t

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

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

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