What is the integral of (2-t)sqrt(t) ?

The integral of (2-t)sqrt(t) is 4/3 t^{3/2}-2/5 t^{5/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (2-t)sqrt(t)

\int (2 - t) t d t

\frac{4}{3} t^{\frac{3}{2}} - \frac{2}{5} t^{\frac{5}{2}} + C

Solution steps

\int (2 - t) t d t

Expand

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

= \int 2 t - t^{\frac{3}{2}} d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 t d t - \int t^{\frac{3}{2}} d t

\int 2 t d t = \frac{4}{3} t^{\frac{3}{2}}

\int t^{\frac{3}{2}} d t = \frac{2}{5} t^{\frac{5}{2}}

= \frac{4}{3} t^{\frac{3}{2}} - \frac{2}{5} t^{\frac{5}{2}}

Add a constant to the solution

= \frac{4}{3} t^{\frac{3}{2}} - \frac{2}{5} t^{\frac{5}{2}} + C

What is the integral of (2-t)sqrt(t) ?
The integral of (2-t)sqrt(t) is 4/3 t^{3/2}-2/5 t^{5/2}+C