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

The integral from-2 to 2 of 2-(x^2-2) is 32/3

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

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

\frac{32}{3}

Decimal

10.66666 \dots

Solution steps

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

Simplify

= \int_{- 2}^{2} - x^{2} + 4 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} x^{2} d x + \int_{- 2}^{2} 4 d x

\int_{- 2}^{2} x^{2} d x = \frac{16}{3}

\int_{- 2}^{2} 4 d x = 16

= - \frac{16}{3} + 16

Simplify

- \frac{16}{3} + 16 : \frac{32}{3}

= \frac{32}{3}

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What is the integral from-2 to 2 of 2-(x^2-2) ?
The integral from-2 to 2 of 2-(x^2-2) is 32/3