Calculus

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

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  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

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  2. Thank you. What about part B?

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