What is the integral from 0 to 2 of 3x(2-x) ?

The integral from 0 to 2 of 3x(2-x) is 4

Popular >

integral from 0 to 2 of 3x(2-x)

\int_{0}^{2} 3 x (2 - x) d x

4

Solution steps

\int_{0}^{2} 3 x (2 - x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int_{0}^{2} x (2 - x) d x

Expand

x (2 - x) : 2 x - x^{2}

= 3 \cdot \int_{0}^{2} 2 x - x^{2} 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

= 3 (\int_{0}^{2} 2 x d x - \int_{0}^{2} x^{2} d x)

\int_{0}^{2} 2 x d x = 4

\int_{0}^{2} x^{2} d x = \frac{8}{3}

= 3 (4 - \frac{8}{3})

Simplify

3 (4 - \frac{8}{3}) : 4

= 4

\int_{0}^{1} 10 x d x

\int_{0}^{3} r^{3} d r

\int_{0}^{1} \frac{x}{3 x + 1} d x

\int_{- 2}^{- 1} \frac{1}{z} (y + \frac{1}{2}) d y

\int_{- 4}^{- 1} (x^{3} + 5 x^{2} + 4 x) d x

What is the integral from 0 to 2 of 3x(2-x) ?
The integral from 0 to 2 of 3x(2-x) is 4