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

The integral from-3 to-2 of (x^5)/4-x^2+3 is -745/24

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

\int_{- 3}^{- 2} \frac{x ^{5}}{4} - x^{2} + 3 d x

- \frac{745}{24}

Decimal Notation

- 31.04166 \dots

Solution steps

\int_{- 3}^{- 2} \frac{x ^{5}}{4} - x^{2} + 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_{- 3}^{- 2} \frac{x ^{5}}{4} d x - \int_{- 3}^{- 2} x^{2} d x + \int_{- 3}^{- 2} 3 d x

\int_{- 3}^{- 2} \frac{x ^{5}}{4} d x = - \frac{665}{24}

\int_{- 3}^{- 2} x^{2} d x = \frac{19}{3}

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

= - \frac{665}{24} - \frac{19}{3} + 3

Simplify

- \frac{665}{24} - \frac{19}{3} + 3 : - \frac{745}{24}

= - \frac{745}{24}

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What is the integral from-3 to-2 of (x^5)/4-x^2+3 ?
The integral from-3 to-2 of (x^5)/4-x^2+3 is -745/24