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

The integral from-1 to 3 of (3+2x-x^2) is 32/3

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

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

\frac{32}{3}

Decimal Notation

10.66666 \dots

Solution steps

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

\int_{- 1}^{3} 3 d x = 12

\int_{- 1}^{3} 2 x d x = 8

\int_{- 1}^{3} x^{2} d x = \frac{28}{3}

= 12 + 8 - \frac{28}{3}

Simplify

12 + 8 - \frac{28}{3} : \frac{32}{3}

= \frac{32}{3}

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What is the integral from-1 to 3 of (3+2x-x^2) ?
The integral from-1 to 3 of (3+2x-x^2) is 32/3