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

The integral from-2 to 2 of (x^2)/2-3 is -28/3

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

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

- \frac{28}{3}

Decimal

- 9.33333 \dots

Solution steps

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

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

\int_{- 2}^{2} 3 d x = 12

= \frac{8}{3} - 12

Simplify

\frac{8}{3} - 12 : - \frac{28}{3}

= - \frac{28}{3}

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What is the integral from-2 to 2 of (x^2)/2-3 ?
The integral from-2 to 2 of (x^2)/2-3 is -28/3