What is the integral from 0 to 4 of (14-x)sqrt(x) ?

The integral from 0 to 4 of (14-x)sqrt(x) is 928/15

Popular >

integral from 0 to 4 of (14-x)sqrt(x)

\int_{0}^{4} (14 - x) x d x

\frac{928}{15}

Decimal

61.86666 \dots

Solution steps

\int_{0}^{4} (14 - x) x d x

Expand

(14 - x) x : 14 x - x^{\frac{3}{2}}

= \int_{0}^{4} 14 x - x^{\frac{3}{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

= \int_{0}^{4} 14 x d x - \int_{0}^{4} x^{\frac{3}{2}} d x

\int_{0}^{4} 14 x d x = \frac{224}{3}

\int_{0}^{4} x^{\frac{3}{2}} d x = \frac{64}{5}

= \frac{224}{3} - \frac{64}{5}

Simplify

\frac{224}{3} - \frac{64}{5} : \frac{928}{15}

= \frac{928}{15}

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

\int_{3}^{6} 30 x^{3} 1 + x^{2} d x

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

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

\int_{0}^{1} \frac{1}{x 1 - x} d x

What is the integral from 0 to 4 of (14-x)sqrt(x) ?
The integral from 0 to 4 of (14-x)sqrt(x) is 928/15