# area between a line and a curve

I presume that you know that the "area under a curve", the area between the graph and the x-axis, between, say, x= a and x= b, is the integral of the function from a to b. In this case, there is only one x bound given but $y= e^{2x}$ goes to 0 as x goes to negative infinity so that the three lines, $y= e^{2x}$, y= 0, and x= 2 do bound a "region". The area is $\int_{-\infty}^2 e^{2x} dx$. Integrate $\int_a^2 e^{2x} dx$ and then take the limit as a goes to negative infinity.