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

- 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_{1}^{5} - x^{2} + 6 x - 5 d x

\int_{0}^{l n (5)} 2 e^{3 x} d x

\int_{- 1}^{1} y^{3} - y d y

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

\int_{0}^{\infty} t e^{- 2 t} d t

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