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

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

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

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

\frac{8}{3}

Decimal Notation

2.66666 \dots

Solution steps

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

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

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

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

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

Simplify

= \frac{8}{3}

\int_{0}^{8} ∣ x - 3 ∣ d x

\int_{0}^{1} 4 x - 6 (x^{2})^{\frac{1}{3}} d x

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

\int_{- 3}^{2} x^{2} - (6 - x) d x

\int_{2}^{4} 8 - 2 x d x

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