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

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

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integral from-5 to 5 of (25-x^2)

\int_{- 5}^{5} (25 - x^{2}) d x

\frac{500}{3}

Decimal Notation

166.66666 \dots

Solution steps

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

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

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

= 250 - \frac{250}{3}

Simplify

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

= \frac{500}{3}

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