What is the integral from-2 to 2 of (-5x^2-4x)^3 ?

The integral from-2 to 2 of (-5x^2-4x)^3 is -53504/7

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integral from-2 to 2 of (-5x^2-4x)^3

\int_{- 2}^{2} (- 5 x^{2} - 4 x)^{3} d x

- \frac{53504}{7}

Decimal

- 7643.42857 \dots

Solution steps

\int_{- 2}^{2} (- 5 x^{2} - 4 x)^{3} d x

Expand

(- 5 x^{2} - 4 x)^{3} : - 125 x^{6} - 300 x^{5} - 240 x^{4} - 64 x^{3}

= \int_{- 2}^{2} - 125 x^{6} - 300 x^{5} - 240 x^{4} - 64 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_{- 2}^{2} 125 x^{6} d x - \int_{- 2}^{2} 300 x^{5} d x - \int_{- 2}^{2} 240 x^{4} d x - \int_{- 2}^{2} 64 x^{3} d x

\int_{- 2}^{2} 125 x^{6} d x = \frac{32000}{7}

\int_{- 2}^{2} 300 x^{5} d x = 0

\int_{- 2}^{2} 240 x^{4} d x = 3072

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

= - \frac{32000}{7} - 0 - 3072 - 0

Simplify

- \frac{32000}{7} - 0 - 3072 - 0 : - \frac{53504}{7}

= - \frac{53504}{7}

What is the integral from-2 to 2 of (-5x^2-4x)^3 ?
The integral from-2 to 2 of (-5x^2-4x)^3 is -53504/7