What is the integral from 0 to 6 of sqrt(6x+64) ?

The integral from 0 to 6 of sqrt(6x+64) is 488/9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 6 of sqrt(6x+64)

\int_{0}^{6} 6 x + 64 d x

\frac{488}{9}

Decimal

54.22222 \dots

Solution steps

\int_{0}^{6} 6 x + 64 d x

Apply u-substitution

= \int_{64}^{100} \frac{u}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int_{64}^{100} u d u

Apply the Power Rule

= \frac{1}{6} [\frac{2}{3} u^{\frac{3}{2}}]_{64}^{100}

Compute the boundaries:

\frac{976}{3}

= \frac{1}{6} \cdot \frac{976}{3}

Simplify

= \frac{488}{9}

What is the integral from 0 to 6 of sqrt(6x+64) ?
The integral from 0 to 6 of sqrt(6x+64) is 488/9