What is the integral from 0 to 2 of (6-t)sqrt(t) ?

The integral from 0 to 2 of (6-t)sqrt(t) is 8sqrt(2)-(8sqrt(2))/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of (6-t)sqrt(t)

\int_{0}^{2} (6 - t) t d t

82 - \frac{8 2}{5}

Decimal Notation

9.05096 \dots

Solution steps

\int_{0}^{2} (6 - t) t d t

Expand

(6 - t) t : 6 t - t^{\frac{3}{2}}

= \int_{0}^{2} 6 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_{0}^{2} 6 t d t - \int_{0}^{2} t^{\frac{3}{2}} d t

\int_{0}^{2} 6 t d t = 82

\int_{0}^{2} t^{\frac{3}{2}} d t = \frac{8 2}{5}

= 82 - \frac{8 2}{5}

\int_{0}^{\infty} e^{- n x} d x

\int_{1}^{N} \frac{1}{x ^{p}} d x

\int_{1}^{3} \frac{7}{x} d x

\int_{1}^{t} x ln (x) d x

\int_{- 5}^{0} 2 + 4 - x + x d x

What is the integral from 0 to 2 of (6-t)sqrt(t) ?
The integral from 0 to 2 of (6-t)sqrt(t) is 8sqrt(2)-(8sqrt(2))/5