What is the integral from-3 to 5 of (2x+15)-x^2 ?

The integral from-3 to 5 of (2x+15)-x^2 is 256/3

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integral from-3 to 5 of (2x+15)-x^2

\int_{- 3}^{5} (2 x + 15) - x^{2} d x

\frac{256}{3}

Decimal

85.33333 \dots

Solution steps

\int_{- 3}^{5} 2 x + 15 - 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_{- 3}^{5} 2 x d x + \int_{- 3}^{5} 15 d x - \int_{- 3}^{5} x^{2} d x

\int_{- 3}^{5} 2 x d x = 16

\int_{- 3}^{5} 15 d x = 120

\int_{- 3}^{5} x^{2} d x = \frac{152}{3}

= 16 + 120 - \frac{152}{3}

Simplify

16 + 120 - \frac{152}{3} : \frac{256}{3}

= \frac{256}{3}

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What is the integral from-3 to 5 of (2x+15)-x^2 ?
The integral from-3 to 5 of (2x+15)-x^2 is 256/3