Let R be the first quadrant region enclosed by y=e^2, y=e^x and the y-axis. The area of region R is?

Question

I don't understand why is the interval is from [0-2].

Thanks

Answer 1

You need the intersection of y = e^x and y = e^2
e^x = e^2
so x = 2

then area = ∫ e^2 - e^x from 0 to 2
= [e^2 x - e^x] from 0 to 2
= 2e^2 - e^2 - (0 - e^0)
= e^2 + 1