What is the integral from 1 to 16 of (x-3)/(sqrt(x)) ?

The integral from 1 to 16 of (x-3)/(sqrt(x)) is 24

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 16 of (x-3)/(sqrt(x))

\int_{1}^{16} \frac{x - 3}{x} d x

24

Solution steps

\int_{1}^{16} \frac{x - 3}{x} d x

Expand

\frac{x - 3}{x} : x - \frac{3}{x}

= \int_{1}^{16} x - \frac{3}{x} 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}^{16} x d x - \int_{1}^{16} \frac{3}{x} d x

\int_{1}^{16} x d x = 42

\int_{1}^{16} \frac{3}{x} d x = 18

= 42 - 18

Simplify

= 24

\int e^{t} sin (t) d t

y^{^{'}} = 1 + 4 y^{2}

\frac{\partial}{\partial t} (e^{2 t})

f (x) = \frac{6 x}{x + 5}, at x = - 3

What is the integral from 1 to 16 of (x-3)/(sqrt(x)) ?
The integral from 1 to 16 of (x-3)/(sqrt(x)) is 24