What is the integral from 0 to 2 of 14^{2x} ?

The integral from 0 to 2 of 14^{2x} is (38415)/(2ln(14))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of 14^{2x}

\int_{0}^{2} 1 4^{2 x} d x

\frac{38415}{2 ln ( 14 )}

Decimal

7278.16701 \dots

Solution steps

\int_{0}^{2} 1 4^{2 x} d x

Simplify

1 4^{2 x} : 19 6^{x}

= \int_{0}^{2} 19 6^{x} d x

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

= [\frac{19 6 ^{x}}{ln ( 196 )}]_{0}^{2}

\frac{19 6 ^{x}}{ln ( 196 )} = \frac{4 9 ^{x} \cdot 2 ^{2 x - 1}}{ln ( 14 )}

= [\frac{4 9 ^{x} \cdot 2 ^{2 x - 1}}{ln ( 14 )}]_{0}^{2}

Compute the boundaries:

\frac{38415}{2 ln ( 14 )}

= \frac{38415}{2 ln ( 14 )}

\int_{0}^{9} 2 x d x

\int_{- 1}^{1} x^{3} - 3 x d x

\int_{0}^{1} \frac{e ^{x}}{5 - e ^{x}} d x

\int_{- 1}^{1} (x^{7} + x^{3} + x) d x

\int_{- 1}^{0} ∣ 3 x + 1 ∣ d x

What is the integral from 0 to 2 of 14^{2x} ?
The integral from 0 to 2 of 14^{2x} is (38415)/(2ln(14))