What is the integral from-3 to 0 of x^3+5x^2+6x ?

The integral from-3 to 0 of x^3+5x^2+6x is -9/4

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integral from-3 to 0 of x^3+5x^2+6x

\int_{- 3}^{0} x^{3} + 5 x^{2} + 6 x d x

- \frac{9}{4}

Decimal

- 2.25

Solution steps

\int_{- 3}^{0} x^{3} + 5 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_{- 3}^{0} x^{3} d x + \int_{- 3}^{0} 5 x^{2} d x + \int_{- 3}^{0} 6 x d x

\int_{- 3}^{0} x^{3} d x = - \frac{81}{4}

\int_{- 3}^{0} 5 x^{2} d x = 45

\int_{- 3}^{0} 6 x d x = - 27

= - \frac{81}{4} + 45 - 27

Simplify

- \frac{81}{4} + 45 - 27 : - \frac{9}{4}

= - \frac{9}{4}

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What is the integral from-3 to 0 of x^3+5x^2+6x ?
The integral from-3 to 0 of x^3+5x^2+6x is -9/4