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

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

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

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

\frac{64}{3}

Decimal

21.33333 \dots

Solution steps

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

Simplify

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

\int_{- 2}^{2} 8 d x = 32

\int_{- 2}^{2} 2 x^{2} d x = \frac{32}{3}

= 32 - \frac{32}{3}

Simplify

32 - \frac{32}{3} : \frac{64}{3}

= \frac{64}{3}

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