What is the integral from 0 to 30 of 4x(30-x) ?

The integral from 0 to 30 of 4x(30-x) is 18000

Popular >

integral from 0 to 30 of 4x(30-x)

\int_{0}^{30} 4 x (30 - x) d x

18000

Solution steps

\int_{0}^{30} 4 x (30 - x) d x

Take the constant out:

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

= 4 \cdot \int_{0}^{30} x (30 - x) d x

Expand

x (30 - x) : 30 x - x^{2}

= 4 \cdot \int_{0}^{30} 30 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

= 4 (\int_{0}^{30} 30 x d x - \int_{0}^{30} x^{2} d x)

\int_{0}^{30} 30 x d x = 13500

\int_{0}^{30} x^{2} d x = 9000

= 4 (13500 - 9000)

Simplify

= 18000

\frac{\partial}{\partial x} (x^{3} e^{4 x y})

y^{^{'}} = \frac{y}{t} - \frac{1}{\frac{y}{t}}

f (x) = x + \frac{2}{x}, at x = 2

\int \frac{50}{x ^{0.25}} d x

\frac{d}{d y} (x e^{x - y})

What is the integral from 0 to 30 of 4x(30-x) ?
The integral from 0 to 30 of 4x(30-x) is 18000