Results 1 to 4 of 4

Math Help - Is this problem solved correctly? (integrals)

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    58

    Is this problem solved correctly? (integrals)

    Question:
    Find a formula for the volume of this trapezoid (rotates 360 degrees around the x-axis):

    R= big radius
    r= small radius
    h= height

    The area is equal to:
    A=\frac{1}{2}\cdot(r+R)\cdot h

    Volume of an object rotating around the x-axis:
    V_x=\pi\cdot\int_{a}^{b}f(x)^2\, dx

    Judging by the graph, it starts from x=0, and it ends on x=h, therefore the interval is [0;h].

    The area function is the equation for a trapezoid, therefore, the function.

    Conclusion:
    V_x=\pi\cdot\int_{0}^{h}(\frac{1}{2}\cdot(r+R)\cdo  t h)^2\, dh

    Did I solve this correctly? I'm afraid, the "dh" is wrong, and generally just unsure if I solved this correctly.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Quote Originally Posted by No Logic Sense View Post
    Question:
    Find a formula for the volume of this trapezoid (rotates 360 degrees around the x-axis):

    R= big radius
    r= small radius
    h= height

    The area is equal to:
    A=\frac{1}{2}\cdot(r+R)\cdot h

    Volume of an object rotating around the x-axis:
    V_x=\pi\cdot\int_{a}^{b}f(x)^2\, dx

    Judging by the graph, it starts from x=0, and it ends on x=h, therefore the interval is [0;h].

    The area function is the equation for a trapezoid, therefore, the function.

    Conclusion:
    V_x=\pi\cdot\int_{0}^{h}(\frac{1}{2}\cdot(r+R)\cdo  t h)^2\, dh

    Did I solve this correctly? I'm afraid, the "dh" is wrong, and generally just unsure if I solved this correctly.
    Hi

    You did not solve correctly !
    V_x=\pi\cdot\int_{a}^{b}f(x)^2\, dx
    This formula is applied to solid whose frontier is generated by the rotation of a curve whose equation is y=f(x) around x axis
    The function to be taken into account is therefore the line joining the point (0,R) to the point (h,r)
    You have to integrate
    V_x=\pi\cdot\int_{0}^{h}(R+\frac{r-R}{h}\cdot x)^2\, dx
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2008
    Posts
    58
    Ah, okay, I understand now. Thank you.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    645
    Hello, No Logic Sense!

    Sorry, wrong set-up . . .


    Find a formula for the volume of this trapezoid (rotates 360 degrees around the x-axis):

    The slope of the slanted line is: m = \tfrac{r-R}{h}

    The equation of the line is: . y \:=\:\tfrac{r-R}{h}x + R

    We want to rotate the area under the line about the x-axis (from 0 to h).

    The formula is: . V \;=\;\pi\int^h_0\left(\tfrac{r-R}{h}x + R\right)^2\,dx

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. is this excercise correctly solved?
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 22nd 2009, 08:44 AM
  2. Replies: 1
    Last Post: April 25th 2009, 02:41 PM
  3. did i solved this limit correctly
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 13th 2009, 10:55 AM
  4. Did I do this problem correctly?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 27th 2007, 11:06 PM
  5. Replies: 3
    Last Post: October 20th 2005, 12:09 AM

Search Tags


/mathhelpforum @mathhelpforum