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

The integral from 0 to 4 of 3x(4-x) is 32

Popular >

integral from 0 to 4 of 3x(4-x)

\int_{0}^{4} 3 x (4 - x) d x

32

Solution steps

\int_{0}^{4} 3 x (4 - 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}^{4} x (4 - x) d x

Expand

x (4 - x) : 4 x - x^{2}

= 3 \cdot \int_{0}^{4} 4 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}^{4} 4 x d x - \int_{0}^{4} x^{2} d x)

\int_{0}^{4} 4 x d x = 32

\int_{0}^{4} x^{2} d x = \frac{64}{3}

= 3 (32 - \frac{64}{3})

Simplify

3 (32 - \frac{64}{3}) : 32

= 32

\int_{0}^{a} e^{- s t} d t

\int_{1}^{3} \frac{1}{x ^{2} - 1} d x

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

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

\int_{π}^{2 π} r sin (r) d r

What is the integral from 0 to 4 of 3x(4-x) ?
The integral from 0 to 4 of 3x(4-x) is 32