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

The integral from 2 to 3 of 2^{2x} is (24)/(ln(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 3 of 2^{2x}

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

\frac{24}{ln ( 2 )}

Decimal

34.62468 \dots

Solution steps

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

Simplify

2^{2 x} : 4^{x}

= \int_{2}^{3} 4^{x} d x

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

= [\frac{4 ^{x}}{ln ( 4 )}]_{2}^{3}

\frac{4 ^{x}}{ln ( 4 )} = \frac{2 ^{2 x - 1}}{ln ( 2 )}

= [\frac{2 ^{2 x - 1}}{ln ( 2 )}]_{2}^{3}

Compute the boundaries:

\frac{24}{ln ( 2 )}

= \frac{24}{ln ( 2 )}

\int_{0}^{7} x e^{x^{2}} d x

\int_{- 1}^{2} x - (x^{2} - 2) d x

\int_{0}^{x} e^{t^{3}} d t

\int_{0}^{1} \frac{t}{t + 1} d t

\int_{0}^{\frac{1}{3}} - 3 x^{2} + x d x

What is the integral from 2 to 3 of 2^{2x} ?
The integral from 2 to 3 of 2^{2x} is (24)/(ln(2))