Posted by **some kid** on Sunday, April 12, 2009 at 7:40pm.

Let R be the first quadrant region enclosed by the graph of y= 2e^-x and the line x=k.

a) Find the area of R in terms of k.

b) Find the volume of the solid generated when R is rotated about the x-axis in terms of k.

c) What is the volume in part (b) as k approaches infinity?

- AP Calculus -
**drwls**, Monday, April 13, 2009 at 8:42am
a) For the first quadrant region, x>0 to x = k, and the enclosed area is

Integral y dx =

Integral 2e^-x dx

x = 0 to k

= -2 e^-k + 2 e^0

= 2(1 - e^-k)

b) Make the integrand pi*y^2 dx and perform the resulting integration from 0 to k

c) This should be obvious after doing (b)

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