Question

Find the area of the region enclosed by the graphs y=e^x , y=e^-4x , x=ln(3)

Answer 1

Can you plot the regions ? (i.e. draw them)

Answer 2

\(\displaystyle \int_0^3 e^{x}\, dx\) gives the area between the curve \( y = e^x \) and the x-axis. ( 1 in the drawing)

\(\displaystyle \int_0^3 e^{-4x} \, dx\) gives the area between the curve \(y = e^{-4x} \) and the x-axis. ( 2 in the drawing)



Subtract the two areas (1 - 2) to get the value of the area enclosed i.e. \(\displaystyle \int_0^3 (e^{x}-e^{-4x})\, dx\)