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Popular Calculus >

integral from-8 to 8 of 64-x^2

Solution

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

Solution

\frac{2048}{3}

+1

Decimal

682.66666 \dots

Solution steps

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

\int_{- 8}^{8} 64 d x = 1024

\int_{- 8}^{8} x^{2} d x = \frac{1024}{3}

= 1024 - \frac{1024}{3}

Simplify

1024 - \frac{1024}{3} : \frac{2048}{3}

= \frac{2048}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-8 to 8 of 64-x^2 ?
The integral from-8 to 8 of 64-x^2 is 2048/3