What is the integral from-4 to 0 of x^3+x^2-6x-6x ?

The integral from-4 to 0 of x^3+x^2-6x-6x is 160/3

Popular >

integral from-4 to 0 of x^3+x^2-6x-6x

\int_{- 4}^{0} x^{3} + x^{2} - 6 x - 6 x d x

\frac{160}{3}

Decimal

53.33333 \dots

Solution steps

\int_{- 4}^{0} x^{3} + x^{2} - 6 x - 6 x d x

Simplify

= \int_{- 4}^{0} x^{3} + x^{2} - 12 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_{- 4}^{0} x^{3} d x + \int_{- 4}^{0} x^{2} d x - \int_{- 4}^{0} 12 x d x

\int_{- 4}^{0} x^{3} d x = - 64

\int_{- 4}^{0} x^{2} d x = \frac{64}{3}

\int_{- 4}^{0} 12 x d x = - 96

= - 64 + \frac{64}{3} - (- 96)

Simplify

- 64 + \frac{64}{3} - (- 96) : \frac{160}{3}

= \frac{160}{3}

\int_{1}^{3} x^{2} + 3 x - 4 d x

\int_{1}^{7} 2 x d x

\int_{\frac{π}{2}}^{2 π} cos (x) d x

\int_{- π}^{π} e^{x} e^{- in x} d x

\int_{1}^{3} x + 6 d x

What is the integral from-4 to 0 of x^3+x^2-6x-6x ?
The integral from-4 to 0 of x^3+x^2-6x-6x is 160/3