Question

the area of the region bounded by the curve y=e^2x the x axis the y axis and the line x=2 is equal toA) e^4/2 -e B) e^4/2 - 1 C) e^4/2 - 1/2 D) 2e^4 -e E) 2e^4 -2

Answer 1

Answer:b

Step-by-step explanation:

Given

$y=e^{2x}$

Area bounded by $y=e^{2x}$, $y=0,\ x=0\ and\ x=2$ is shown by shaded area in the diagram

$Area=A=\int_{0}^{2}ydx$

$A=\int_{0}^{2}e^{2x}dx$

$A=\left [ \frac{e^{2x}}{2}\right ]^{2}_{0}$

$A=\frac{1}{2}\left [ e^4-e^0\right ]$

$A=\frac{e^4}{2}-1$

thus option b is correct