Question

The area bounded by the curves $y=2^x$,$y=2x-x^2$ between the lines $x=0,x=2$ is

• A. $\frac{3}{\log 2}-\frac{4}{3}$ sq. units
• B. $\frac{3}{\log 2}+\frac{4}{3}$ sq.units
• C. $3-4\log 2$ sq. units
• D. $\frac{4}{3}-\frac{3}{\log 2}$ sq.units

Answer 1

The correct option is A $\frac{3}{\log 2}-\frac{4}{3}$ sq. units

$y=2^x$ , $y=2x-x^2$
$\stackrel{2}{\underset{0}{\int }}{2}^{x}dx-\stackrel{2}{\underset{0}{\int }}(2x-x^2)dx$
$\frac{2^x}{\log 2}{|{}_0^2-(x^2-\frac{x^3}{3})|}_0^2$
$\frac{3}{\log 2}-[4-\frac{8}{3}]$
$=(\frac{3}{\log 2}-4/3)squnits.$