Given y = e^x
a) Find the area under the curve between x = 1 and x=5
b) what is the volume when the curve is rotated on the x-axis between x = 1 and x = 5
area =
= e^x | from 1 to 5
= e^5 - e^1
= ...
volume = π∫ y^2 dx from 1 to 5
= π∫ e^2x dx from 1 to 5
= (1/2)π [ e^2x] from 1 to 5
= (1/2)(e^10 - e^2)
= ...