Calculus AP - Volume of Revolution

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

  1. 👍 0
  2. 👎 0
  3. 👁 134
asked by Kira

Respond to this Question

First Name

Your Response

Similar Questions

  1. algebra 1

    At Jack's Laundromat, 6 of the washers must be replaced. These washers represent of the total number of washers. If w represents the total number of washers, which equation could be used to determine the value of w?

    asked by Alex on March 20, 2014
  2. math

    At a laundromat there is 1 more dryer than there are washers. Write a rule to find the number of d dryers for every w washers.

    asked by Marsha on March 22, 2010
  3. statistics

    The inside diameter of metal washers produced by a company are normally distributed with a mean of .5 inches and a standdrd deviation of .01 inches. Of all washers produced .8% of the washers are rejected because they are too

    asked by josh on June 28, 2014
  4. statistics and probability

    A company manufactures washers, about 5% of which are defective. If a random sample of 100 washers are inspected, what is the probability that fewer than 4 are defective?

    asked by ashley on November 2, 2014
  5. Chemistry

    Merchants usually sell small nuts, washers, and bolts by weight (like jelly beans!) rather than by individually counting the items. Suppose a particular type of washer weighs 0.128 g on the average. What would 130. such washers

    asked by Teresa on December 5, 2014
  6. Calculus AB (AP)

    Hi, I have a calculus test tomorrow and I understand how to complete all of the problems, but I am unsure behind the reasoning of taking two derivatives. Can someone please explain the following: 1. g(x)=e^(f(x))

    asked by Jake on April 13, 2011
  7. Finite Math

    Fifty percent of students enrolled in calculus class have previously taken pre-calculus. Thirty percent of these students received an A for the calculus class, whereas twenty percent of the other students received an A for

    asked by Nikole on June 10, 2015
  8. Calculus

    What is the use of Calculus? How is it use in jobs? What jobs use Calculus? Calculus is used in engineering, economics, any physical science, and in business (e.g., actuary studies and statistics).

    asked by Anonymous on May 5, 2007
  9. statistics and probability

    5. A fastener company is supplying washers to a manufacturer of kitchen appliances who has specified that the outside diameter be 0.500 ± 0.025 inch. Measurements made on 250 washers show that the process is in good statistical

    asked by faye on February 14, 2017
  10. math

    8. In an interview of 50 math majors, 12 liked calculus and geometry 18 liked calculus but not algebra 4 liked calculus, algebra, and geometry 25 liked calculus 15 liked geometry 10 liked algebra but neither calculus nor geometry

    asked by poo on November 30, 2009
  11. Algebra

    In an interview of 50 math majors, 12 liked calculus and geometry 18 liked calculus but not algebra 4 liked calculus, algebra and geometry 25 liked calculus 15 liked geometry 10 liked algebra but neither calculus nor geometry 2

    asked by Anita on January 11, 2010

More Similar Questions