Calculus AP - Volume of Revolution

posted by .

Hi. I have a few calculus problems that I have to do using the washers and shell method to find out what the volume of the graph rotated is. I'll post one question at a time with my work. The problem is, I should be getting the same answer for the problem with the shell method and the washer method, but I'm getting two different answers. If someone could check my work, it would be GREATLY appreciated! And please keep explanations in as easy a form as you can. I'm having a really hard time understanding these concepts. THANKS!!!

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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. please help calculus

    find the volume of the solid formed by revolving the region bounded by y=e^x, y=0, x=o and x=1 about the y axis by using the shell method, i got v=2*pi int(o to 1) (x)(e^x) dx and my teacher said the answer is e/2 but i keep getting …
  2. Math

    Hi, I have to do a project on the Shell Method in my Geometry class. I have been trying to find information on that topic, but have no luck... can someone point me to the right direction as of what keyword to search for, or is there …
  3. Calculus - Find volume of cylinder

    There is a cylindrical tank lying horizontally on the ground, its diameter is 8 feet, and length is 25 feet, the depth of the water currently in the tank is 2 feet. (1 gallon=231 cubic inches) How many gallons of water are in the tank?
  4. calculus

    The volume of the solid obtained by rotating the region enclosed by y=x^2 y=2x about the line x=2 can be computed using the method of disks or washers via an integral The volume is V
  5. calculus

    The volume of the solid obtained by rotating the region enclosed by y=x^2 y=2x about the line x=2 can be computed using the method of disks or washers via an integral The volume is V
  6. Calculus - Volume By Integration

    Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the y-axis: y=(x-2)^3-2, x=0, y=25 Solve by either the disk or washer method. I calculated the volume using the shell method …
  7. calculus

    the region bounded by the graph f(x)=x(2-x) and the x axis is revolved about the y axis. Find the volume of the solid. I did the integral using the shell method, but the answer wasn't correct.
  8. Calculus

    The region enclosed by the graph e^(x/2), y=1, and x=ln(3) is revolved around the x-axis. Find the volume of the solid generated. I don't understand if we have to use the washer method or the disk method for this one because when I …
  9. Calculus

    The region enclosed by the graph e^(x/2), y=1, and x=ln(3) is revolved around the x-axis. Find the volume of the solid generated. I don't understand if we have to use the washer method or the disk method for this one because when I …
  10. Calculus II: Finding the volume of a revolution

    Question: Find the volume of revolution bounded by y-axis, y=cos(x), and y=sin(x) about the horizontal axis. Since the rotation is happening at the horizontal axis, I thought the limits of integration would be [-1,1] and if the curves …

More Similar Questions