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

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

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integral from 0 to 2 of (x^3)/3+x^2-3x

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

- 2

Solution steps

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

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

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

\int_{0}^{2} 3 x d x = 6

= \frac{4}{3} + \frac{8}{3} - 6

Simplify

\frac{4}{3} + \frac{8}{3} - 6 : - 2

= - 2

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