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)

## Answer this Question

## Related Questions

- calculus - Let R be the region in the first quadrant that is enclosed by the ...
- Calculus - Let f be the function given by f(x)=(x^3)/4 - (x^2)/3 - x/2 + 3cosx. ...
- calculus - Find the area of the region in the first quadrant enclosed by the ...
- calculus - Which has more area, the region in the first quadrant enclosed by the...
- calculus - 1. Let R be the region in the first quadrant enclosed by the graphs ...
- Calculus - Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2...
- Calculus 1 - Let f be the function given by f(x)=3sqrt(x-2). A) On the axes ...
- Calculus - Let R be the region in the first quadrant under the graph of y=1/sqrt...
- calculus - Sketch the region in the first quadrant enclosed by y=6/x, y=2x, and ...
- Calculus - This problem set is ridiculously hard. I know how to find the volume ...

More Related Questions