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December 19, 2014

December 19, 2014

Posted by **Kira** on Monday, March 5, 2007 at 7:32pm.

1. Find the volume of the solid that results when the region bounded by y=x and y=x^2 from x=0 and x=1, is resolved about the x axis. Apply both the shell and washer method to solve.

My work:

SHELL:

h=y

r=sqrt(y)

2pi(INT from 0 to 1)y*sqrt(y)dy

2pi(INT from 0 to 1)y^3/2dy

2pi[2/5y^5/2]from 0 to 1

4pi/5 ANSWER

WASHER METHOD:

R=x

r=x^2

pi(INT from 0 to 1)x^2-x^4 dx

pi[1/3x^3 - 1/5x^5]from 0 to 1

pi[5/15 - 3/15]

2pi/15 ANSWER

I don't know how to do shell method, but, I'd say do it on your calculator and see which answer is right and go from there

Your second answer is right. In the first one, the hight is y but the radius is (sqrt(y)-y). Look at a graph to see why. So:

2pi(INT from 0 to 1)y(sqrt(y)-y)dy

2pi(INT from 0 to 1)[y^(3/2)-y^2]dy

2pi[(2/5)y^(5/2)-(1/3)y^3]

=2pi/5 Answer

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