Wednesday

April 1, 2015

April 1, 2015

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

**Answer this Question**

**Related Questions**

Math - Hi, I have to do a project on the Shell Method in my Geometry class. I ...

Calculus - Volume By Integration - Find the volume of the solid generated by ...

calculus - The volume of the solid obtained by rotating the region enclosed by ...

calculus - The volume of the solid obtained by rotating the region enclosed by...

Calculus - Find the volume using the shell method - about the x-axis x=y^2/3

Calculus - Find volume of cylinder - There is a cylindrical tank lying ...

Calculus - Volume by Integration - Find the volume of the solid generated by ...

Calculus - *Note I reposted this question as I changed the subject** The Region...

Calculus - The area is bounded by y= x^3, x= 2 is rotated around the x-axis. ...

please help calculus - find the volume of the solid formed by revolving the ...