What is the integral from-5 to 5 of-x^2+25 ?

The integral from-5 to 5 of-x^2+25 is 500/3

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integral from-5 to 5 of-x^2+25

\int_{- 5}^{5} - x^{2} + 25 d x

\frac{500}{3}

Solution steps

\int_{- 5}^{5} - x^{2} + 25 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_{- 5}^{5} x^{2} d x + \int_{- 5}^{5} 25 d x

\int_{- 5}^{5} x^{2} d x = \frac{250}{3}

\int_{- 5}^{5} 25 d x = 250

= - \frac{250}{3} + 250

Simplify

- \frac{250}{3} + 250 : \frac{500}{3}

= \frac{500}{3}

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What is the integral from-5 to 5 of-x^2+25 ?
The integral from-5 to 5 of-x^2+25 is 500/3