Question

The following are about an infinite region in the 1st quadrant between y=e^-x and the x-axis.

A) Find the area of the region

B)Find the volume of the solid generated by revolving the region about the y-axis

Answer 1

area = integral ( e^-x) from 0 to infinitiy
= [ - e^-x] from 0 to infinity
= [-1/e^x] from 0 to infinity

now clearly as x ---> ∞ , 1/e^x --> 0
so we have
( 0 - (-1/1)
= 1

Answer 2

Thank you. What about part B?