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

Popular >

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}

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}

\int_{- 1}^{1} x^{- 1} d x

\int_{0}^{π} x^{4} cos (2 x^{5}) d x

\int_{1}^{2} y^{2} d y

\int_{3}^{6} 2 d x

\int_{- 5}^{7} (2 x - 1) d x

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