What is the integral from-2 to 0 of x^3-x^2-6x ?

The integral from-2 to 0 of x^3-x^2-6x is 16/3

Popular >

integral from-2 to 0 of x^3-x^2-6x

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

\frac{16}{3}

Decimal

5.33333 \dots

Solution steps

\int_{- 2}^{0} x^{3} - x^{2} - 6 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_{- 2}^{0} x^{3} d x - \int_{- 2}^{0} x^{2} d x - \int_{- 2}^{0} 6 x d x

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

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

\int_{- 2}^{0} 6 x d x = - 12

= - 4 - \frac{8}{3} - (- 12)

Simplify

- 4 - \frac{8}{3} - (- 12) : \frac{16}{3}

= \frac{16}{3}

\frac{\partial}{\partial x} (t^{- 3} \frac{x ^{2}}{2 t})

\int x^{- \frac{5}{3}} d x

\int \frac{\frac{10}{9} x + 14}{x ^{2} + 9} d x

\int \frac{sinh ( ln ( x ) )}{x} d x

x \to + 0 lim (\frac{∣ x - 3 ∣}{x - 3})

What is the integral from-2 to 0 of x^3-x^2-6x ?
The integral from-2 to 0 of x^3-x^2-6x is 16/3