What is the integral from 1 to 4 of x(2-sqrt(x)) ?

The integral from 1 to 4 of x(2-sqrt(x)) is 13/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 1 to 4 of x(2-sqrt(x))

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

\frac{13}{5}

Decimal

2.6

Solution steps

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

Expand

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

= \int_{1}^{4} 2 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_{1}^{4} 2 x d x - \int_{1}^{4} x^{\frac{3}{2}} d x

\int_{1}^{4} 2 x d x = 15

\int_{1}^{4} x^{\frac{3}{2}} d x = \frac{62}{5}

= 15 - \frac{62}{5}

Simplify

15 - \frac{62}{5} : \frac{13}{5}

= \frac{13}{5}

What is the integral from 1 to 4 of x(2-sqrt(x)) ?
The integral from 1 to 4 of x(2-sqrt(x)) is 13/5