What is the integral from-2 to 2 of (x^2)/3-4/3 ?

The integral from-2 to 2 of (x^2)/3-4/3 is -32/9

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integral from-2 to 2 of (x^2)/3-4/3

\int_{- 2}^{2} \frac{x ^{2}}{3} - \frac{4}{3} d x

- \frac{32}{9}

Decimal

- 3.55555 \dots

Solution steps

\int_{- 2}^{2} \frac{x ^{2}}{3} - \frac{4}{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}}{3} d x - \int_{- 2}^{2} \frac{4}{3} d x

\int_{- 2}^{2} \frac{x ^{2}}{3} d x = \frac{16}{9}

\int_{- 2}^{2} \frac{4}{3} d x = \frac{16}{3}

= \frac{16}{9} - \frac{16}{3}

Simplify

\frac{16}{9} - \frac{16}{3} : - \frac{32}{9}

= - \frac{32}{9}

What is the integral from-2 to 2 of (x^2)/3-4/3 ?
The integral from-2 to 2 of (x^2)/3-4/3 is -32/9