Results 1 to 7 of 7
Like Tree1Thanks
  • 1 Post By Prove It

Math Help - Hey. I'm Chloe:) Please help with some integration problems???

  1. #1
    Newbie
    Joined
    May 2013
    From
    Melbourne
    Posts
    6

    Hey. I'm Chloe:) Please help with some integration problems???

    1. A glass vase has the shape of the solid obtained by rotating about the y–axis the area inthe first quadrant lying over the x–interval [0,a] and under the graph of y = x^2.
    Determine how much glass is contained in the vase.

    2. Is the following statement true or false? Justify your answer.
    (Upper limit b, lower limit a) ∫ba f(x) dx 0 implies f (x)0 on [a,b]


    3. Solve the differential equation (dy/dx) = (4xy) / (1+x^2)

    4. Find the unique function y(x) satisfying the differential equation with initial condition
    (dy/dx) - (x^2)y = 0, y(1) = 1



    Thank you. Any Help with the questions is greatly appreciated!
    Last edited by cchloe93; May 15th 2013 at 11:50 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Feb 2013
    From
    Saudi Arabia
    Posts
    441
    Thanks
    86

    Re: Hey. I'm Chloe:) Please help with some integration problems???

    Chloe

    1. find the volume of the glass by calculating the integral π(ydy) from 0 to a^2.

    2. No it is not correct .The integral f(x) from a to b being < 0 simply means that the total area + and - gives a negative result but the function f(x) might be positive

    3. separate the variables and get dy/y =4x/(1+x^2) then integrate....it is easy

    4. separate the variables again and find dy/y=x^2dx then integrate and use x=1 ,y=1 to find the constant C of integration.

    good luck
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2013
    From
    Melbourne
    Posts
    6

    Re: Hey. I'm Chloe:) Please help with some integration problems???

    Would this working for qn 1 be correct?

    V = ∫(x = 0 to a) 2πx * x^2 dx
    ..= ∫(x = 0 to a) 2πx^3 dx
    ..= 2πx^4/4 {for x = 0 to a}
    ..= (π/2)a^4.

    It looks similar to what you've mentioned but its w.r.t. x instead of y.

    Also, what kind of functions would prove the statement false?

    A modulus function is all i can think of, and i'm not too sure thats right either.

    Thanks a lot for helping
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Feb 2013
    From
    Saudi Arabia
    Posts
    441
    Thanks
    86

    Re: Hey. I'm Chloe:) Please help with some integration problems???

    Chloee
    yes the answer is ..= (π/2)a^4.
    but when you compute volumes by rotating curves over the y-axis you must get directly the integral πx^2dy from a to b ( the limits of integration ,in your case 0 and a^2.
    download this file for a quick revision on this subject.

    http://www.mathcentre.ac.uk/resource...mes-2009-1.pdf

    MINOAS
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,792
    Thanks
    1532

    Re: Hey. I'm Chloe:) Please help with some integration problems???

    The first problem, "Determine how much glass is contained in the vase", does not, to me, seem to ask for the volume of the figure! A vase, is, after all, hollow so that you can put things, like flowers, in it. It seems to me it should be a surface area multiplied by the thickness of the glass- but we are not told any thickness.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    May 2013
    From
    Melbourne
    Posts
    6

    Re: Hey. I'm Chloe:) Please help with some integration problems???

    But what we're calculating is the volume of the figure isn't it? All we're doing is just subbing it into the formula for volume...

    For the second question, is there an example of functions that prove the statement false?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,591
    Thanks
    1445

    Re: Hey. I'm Chloe:) Please help with some integration problems???

    I'd like to point out to the OP that you should not post any more than two questions per thread, and you must show that you have made an effort for each question by posting your working and pointing out exactly where you are stuck.

    I completely agree with HallsofIvy that the first question is ambiguous. However, the amount of glass used WOULD be a volume. The trouble is that we don't know the THICKNESS of the glass, which means we can not tell how much volume needs to be subtracted from the total solid volume you have found in order to hollow it out. I suggest you speak to your lecturer to determine exactly what is expected in this question.
    Thanks from Paze
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: November 3rd 2010, 12:54 AM
  2. Problems with integration word problems
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 25th 2010, 05:39 PM
  3. integration problems
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 20th 2009, 04:01 AM
  4. Integration Problems
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 16th 2008, 04:44 PM
  5. plz help! Integration problems
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 18th 2008, 06:15 AM

Search Tags


/mathhelpforum @mathhelpforum