What is the integral from 0.5 to 1.5 of (14^{2x}) ?

The integral from 0.5 to 1.5 of (14^{2x}) is 517.23014…

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integral from 0.5 to 1.5 of (14^{2x})

\int_{0.5}^{1.5} (1 4^{2 x}) d x

517.23014 \dots

Solution steps

\int_{0.5}^{1.5} 1 4^{2 x} d x

Simplify

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

= \int_{0.5}^{1.5} 19 6^{x} d x

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

= [\frac{19 6 ^{x}}{ln ( 196 )}]_{0.5}^{1.5}

\frac{19 6 ^{x}}{ln ( 196 )} = 0.18946 \dots \cdot 19 6^{x}

= [0.18946 \dots \cdot 19 6^{x}]_{0.5}^{1.5}

Compute the boundaries:

517.23014 \dots

= 517.23014 \dots

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What is the integral from 0.5 to 1.5 of (14^{2x}) ?
The integral from 0.5 to 1.5 of (14^{2x}) is 517.23014…