What is the integral from-3 to-1 of (x^2+x+7) ?

The integral from-3 to-1 of (x^2+x+7) is 56/3

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integral from-3 to-1 of (x^2+x+7)

\int_{- 3}^{- 1} (x^{2} + x + 7) d x

\frac{56}{3}

Decimal Notation

18.66666 \dots

Solution steps

\int_{- 3}^{- 1} x^{2} + x + 7 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}^{- 1} x^{2} d x + \int_{- 3}^{- 1} x d x + \int_{- 3}^{- 1} 7 d x

\int_{- 3}^{- 1} x^{2} d x = \frac{26}{3}

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

\int_{- 3}^{- 1} 7 d x = 14

= \frac{26}{3} - 4 + 14

Simplify

\frac{26}{3} - 4 + 14 : \frac{56}{3}

= \frac{56}{3}

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What is the integral from-3 to-1 of (x^2+x+7) ?
The integral from-3 to-1 of (x^2+x+7) is 56/3