What is the integral from 0 to 2 of sqrt(2x+1) ?

The integral from 0 to 2 of sqrt(2x+1) is (5sqrt(5)-1)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 2 of sqrt(2x+1)

\int_{0}^{2} 2 x + 1 d x

\frac{5 5 - 1}{3}

Decimal

3.39344 \dots

Solution steps

\int_{0}^{2} 2 x + 1 d x

Apply u-substitution

= \int_{1}^{5} \frac{u}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{1}^{5} u d u

Apply the Power Rule

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{5}

Compute the boundaries:

\frac{10 5}{3} - \frac{2}{3}

= \frac{1}{2} (\frac{10 5}{3} - \frac{2}{3})

Simplify

= \frac{5 5 - 1}{3}

What is the integral from 0 to 2 of sqrt(2x+1) ?
The integral from 0 to 2 of sqrt(2x+1) is (5sqrt(5)-1)/3