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

The integral from-2 to 3 of ((x^2)/3-4) is -145/9

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

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

- \frac{145}{9}

Decimal

- 16.11111 \dots

Solution steps

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

\int_{- 2}^{3} \frac{x ^{2}}{3} d x = \frac{35}{9}

\int_{- 2}^{3} 4 d x = 20

= \frac{35}{9} - 20

Simplify

\frac{35}{9} - 20 : - \frac{145}{9}

= - \frac{145}{9}

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What is the integral from-2 to 3 of ((x^2)/3-4) ?
The integral from-2 to 3 of ((x^2)/3-4) is -145/9