What is the integral from 0 to 8 of (64-x^2) ?

The integral from 0 to 8 of (64-x^2) is 1024/3

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integral from 0 to 8 of (64-x^2)

\int_{0}^{8} (64 - x^{2}) d x

\frac{1024}{3}

Decimal

341.33333 \dots

Solution steps

\int_{0}^{8} 64 - 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_{0}^{8} 64 d x - \int_{0}^{8} x^{2} d x

\int_{0}^{8} 64 d x = 512

\int_{0}^{8} x^{2} d x = \frac{512}{3}

= 512 - \frac{512}{3}

Simplify

512 - \frac{512}{3} : \frac{1024}{3}

= \frac{1024}{3}

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What is the integral from 0 to 8 of (64-x^2) ?
The integral from 0 to 8 of (64-x^2) is 1024/3