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

The integral from 2 to 4 of (x/2-(2x^2)/3) is -85/9

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

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

- \frac{85}{9}

Decimal

- 9.44444 \dots

Solution steps

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

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

\int_{2}^{4} \frac{2 x ^{2}}{3} d x = \frac{112}{9}

= 3 - \frac{112}{9}

Simplify

3 - \frac{112}{9} : - \frac{85}{9}

= - \frac{85}{9}

What is the integral from 2 to 4 of (x/2-(2x^2)/3) ?
The integral from 2 to 4 of (x/2-(2x^2)/3) is -85/9