What is the integral from-4 to 5 of-x^2+x+20 ?

The integral from-4 to 5 of-x^2+x+20 is 243/2

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integral from-4 to 5 of-x^2+x+20

\int_{- 4}^{5} - x^{2} + x + 20 d x

\frac{243}{2}

Decimal

121.5

Solution steps

\int_{- 4}^{5} - x^{2} + x + 20 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_{- 4}^{5} x^{2} d x + \int_{- 4}^{5} x d x + \int_{- 4}^{5} 20 d x

\int_{- 4}^{5} x^{2} d x = 63

\int_{- 4}^{5} x d x = \frac{9}{2}

\int_{- 4}^{5} 20 d x = 180

= - 63 + \frac{9}{2} + 180

Simplify

- 63 + \frac{9}{2} + 180 : \frac{243}{2}

= \frac{243}{2}

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What is the integral from-4 to 5 of-x^2+x+20 ?
The integral from-4 to 5 of-x^2+x+20 is 243/2