What is the integral from-3 to 2 of 6x-x^2-x^3 ?

The integral from-3 to 2 of 6x-x^2-x^3 is -125/12

Popular >

integral from-3 to 2 of 6x-x^2-x^3

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

- \frac{125}{12}

Decimal

- 10.41666 \dots

Solution steps

\int_{- 3}^{2} 6 x - x^{2} - x^{3} 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_{- 3}^{2} 6 x d x - \int_{- 3}^{2} x^{2} d x - \int_{- 3}^{2} x^{3} d x

\int_{- 3}^{2} 6 x d x = - 15

\int_{- 3}^{2} x^{2} d x = \frac{35}{3}

\int_{- 3}^{2} x^{3} d x = - \frac{65}{4}

= - 15 - \frac{35}{3} - (- \frac{65}{4})

Simplify

- 15 - \frac{35}{3} - (- \frac{65}{4}) : - \frac{125}{12}

= - \frac{125}{12}

\int_{2}^{6} 5 x d x

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

\int_{0}^{l n (u)} 2 e^{- 2 y} d y

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

\int_{1}^{\infty} e^{- a x} d x

What is the integral from-3 to 2 of 6x-x^2-x^3 ?
The integral from-3 to 2 of 6x-x^2-x^3 is -125/12