What is the integral from 3 to 7 of xsqrt(x-3) ?

The integral from 3 to 7 of xsqrt(x-3) is 144/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 3 to 7 of xsqrt(x-3)

\int_{3}^{7} x x - 3 d x

\frac{144}{5}

Decimal

28.8

Solution steps

\int_{3}^{7} x x - 3 d x

Apply u-substitution

= \int_{0}^{4} (u + 3) u d u

Expand

(u + 3) u : u^{\frac{3}{2}} + 3 u

= \int_{0}^{4} u^{\frac{3}{2}} + 3 u d u

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} u^{\frac{3}{2}} d u + \int_{0}^{4} 3 u d u

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

\int_{0}^{4} 3 u d u = 16

= \frac{64}{5} + 16

Simplify

\frac{64}{5} + 16 : \frac{144}{5}

= \frac{144}{5}

What is the integral from 3 to 7 of xsqrt(x-3) ?
The integral from 3 to 7 of xsqrt(x-3) is 144/5