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

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

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

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

\frac{32}{3}

Decimal

10.66666 \dots

Solution steps

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

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

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

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

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

Simplify

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

= \frac{32}{3}

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