Answer: 15 sq. units
Step-by-step explanation:
Given
[tex]f(x)=\ln (2)2^x[/tex]
The area bound by it from x=0 to x=4
Using integration
[tex]I=\int_{0}^{4}f(x)dx[/tex]
[tex]I=\int_{0}^{4}\ln(2)2^xdx[/tex]
[tex]I=\left [ \dfrac{\ln (2)2^x}{\ln (2)} \right ]_0^4[/tex]
[tex]I=\left [ 2^x \right ]_0^4[/tex]
[tex]I=2^4-2^0\\I=16-1=15\ sq.units[/tex]
