Question

Evaluate ${\int }_1^4{4}^{x}dx$

Answer 1

Let us consider the problem:

Using

$\int a^{x}dx=\frac{a^x}{\ln a}$

$=\frac{4^x}{\ln \left(4\right)}$

Simplify,

$={\left[\frac{2^{2x-1}}{\ln \left(2\right)}+C\right]}_1^4$

Compute the boundries

$=\frac{128}{\ln \left(2\right)}\frac{-2}{\ln \left(2\right)}$

$=\frac{124}{\ln \left(2\right)}$