What is the integral from-4 to-1 of (x^3+2x^2+1) ?

The integral from-4 to-1 of (x^3+2x^2+1) is -75/4

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integral from-4 to-1 of (x^3+2x^2+1)

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

- \frac{75}{4}

Decimal Notation

- 18.75

Solution steps

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

\int_{- 4}^{- 1} x^{3} d x = - \frac{255}{4}

\int_{- 4}^{- 1} 2 x^{2} d x = 42

\int_{- 4}^{- 1} 1 d x = 3

= - \frac{255}{4} + 42 + 3

Simplify

- \frac{255}{4} + 42 + 3 : - \frac{75}{4}

= - \frac{75}{4}

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What is the integral from-4 to-1 of (x^3+2x^2+1) ?
The integral from-4 to-1 of (x^3+2x^2+1) is -75/4