What is the integral from 0 to 7 of sqrt(1+9x) ?

The integral from 0 to 7 of sqrt(1+9x) is 1022/27

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 7 of sqrt(1+9x)

\int_{0}^{7} 1 + 9 x d x

\frac{1022}{27}

Decimal

37.85185 \dots

Solution steps

\int_{0}^{7} 1 + 9 x d x

Apply u-substitution

= \int_{1}^{64} \frac{u}{9} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int_{1}^{64} u d u

Apply the Power Rule

= \frac{1}{9} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{64}

Compute the boundaries:

\frac{1022}{3}

= \frac{1}{9} \cdot \frac{1022}{3}

Simplify

= \frac{1022}{27}

What is the integral from 0 to 7 of sqrt(1+9x) ?
The integral from 0 to 7 of sqrt(1+9x) is 1022/27