What is the integral from 0 to 2 of 2^{3x} ?

The integral from 0 to 2 of 2^{3x} is (21)/(ln(2))

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 2^{3x}

\int_{0}^{2} 2^{3 x} d x

\frac{21}{ln ( 2 )}

Decimal

30.29659 \dots

Solution steps

\int_{0}^{2} 2^{3 x} d x

Simplify

2^{3 x} : 8^{x}

= \int_{0}^{2} 8^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= [\frac{8 ^{x}}{ln ( 8 )}]_{0}^{2}

Simplify

ln (8) : 3 ln (2)

= [\frac{8 ^{x}}{3 ln ( 2 )}]_{0}^{2}

Compute the boundaries:

\frac{21}{ln ( 2 )}

= \frac{21}{ln ( 2 )}

What is the integral from 0 to 2 of 2^{3x} ?
The integral from 0 to 2 of 2^{3x} is (21)/(ln(2))