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c3 Volumes of revolution question I don't understand. Help

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    Question 1:
    curve y=x^2 +1. Rotated round the y axis and bounded by the y axis and the line y=4.

    I assumed this meant between y=0 and y=4.

    I keep on getting 4 pie for the answer but in the back of the book the answer is:4.5pie. Dont understand how they got this and Im getting all other revolution questions right with my method.



    Question 2:
    Curve:
    x= e^y +1 rotated round y axis between y= 0 and y=ln2
    I get answer 5 pie. Book has answer 7/2pie + pie ln2.


    Help please.
  2. Offline

    Question 1
    If you draw a sketch of the graph of y=x^2+1 then you'll notice that it intersects the y-axis at y=1 and not y=0, so your integration limits should be 1 \le y \le 4 rather than 0 \le y \le 4.

    Question 2
    Show your working; I agree with the book's answer.

    (P.S. this is pi: \pi, and this is pie: click.)
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    (Original post by Yasin-Ali)
    Question 1:
    curve y=x^2 +1. Rotated round the y axis and bounded by the y axis and the line y=4.

    I assumed this meant between y=0 and y=4.
    .
    It seems odd to be bounded by y axis. Does the question actually say that
    ?
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    (Original post by steve2005)
    It seems odd to be bounded by y axis. Does the question actually say that
    ?
    It seems normal to me; after all, it's being rotated about the y-axis.
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    What exam board is this?
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    Gotta be careful here; as Nuodai pointed out.

    I always tend to draw sketches for these types of questions, incase they niggle a sneaky trick in there (don't just assume the integral).
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    (Original post by steve2005)
    It seems odd to be bounded by y axis. Does the question actually say that
    ?
    Its not very odd.

    In edexcel they only give questions involving rotations of 360deg on the x-axis, but a few questions in the book do have the y-axis rotation questions and it is mentioned that such questions won't come up in the exam.
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    (Original post by raheem94)
    Its not very odd.

    In edexcel they only give questions involving rotations of 360deg on the x-axis, but a few questions in the book do have the y-axis rotation questions and it is mentioned that such questions won't come up in the exam.
    Since the rotation is about the y axis, it does not make sense to say it is bounded by the y axis.

    I have done the question and it's easy never-the-less I'm 99.9% certain there is something wrong with the way the OP has given the question.
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    (Original post by steve2005)
    Since the rotation is about the y axis, it does not make sense to say it is bounded by the y axis.

    I have done the question and it's easy never-the-less I'm 99.9% certain there is something wrong with the way the OP has given the question.
    Hmm, I think the wording is fine.

    Although I suspect, the OP should also say the region is bounded by the curve too.
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    (Original post by f1mad)
    Hmm, I think the wording is fine.

    Although I suspect, the OP should also say the region is bounded by the curve too.
    It is not bounded by the y axis. Sketch and you will see.
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    (Original post by steve2005)
    Since the rotation is about the y axis, it does not make sense to say it is bounded by the y axis.

    I have done the question and it's easy never-the-less I'm 99.9% certain there is something wrong with the way the OP has given the question.
    The OP has not written down the exact question.

    If he would have written down the exact question then the question would have probably said that it is rotated by 360(or 2 pi).
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    (Original post by steve2005)
    It is not bounded by the y axis. Sketch and you will see.
    It is.

    The question should read: the region bounded by the y axis, the line y=4 and the curve y= x^2+1.

    Then there's a distinct region that is clearly bounded by all 3 restrictions.
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    (Original post by f1mad)
    It is.

    The question should read: the region bounded by the y axis, the line y=4 and the curve y= x^2+1.

    Then there's a distinct region that is clearly bounded by all 3 restrictions.
    Yes, I agree with this but that is not what the OP wrote.
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    you can get the volume by revolving around the y - axis, by using the formula:

    V = 2Pi [integal from x=a to x=b of{x f(x)}]dx a and b corresponding to where y=c and y=d.
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    (Original post by Hasufel)
    you can get the volume by revolving around the y - axis, by using the formula:

    V = 2Pi [integal from x=a to x=b of{x f(x)}]dx a and b corresponding to where y=c and y=d.
    This is not correct. For a start it should be pi and not 2 pi, and in this case the limits are y=1 and y =4.
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    Yes it is - try it!

    I`m saying it`s a different WAY of doing it.

    It is correct. QED
  17. Offline

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    (Original post by steve2005)
    This is not correct. For a start it should be pi and not 2 pi, and in this case the limits are y=1 and y =4.
    http://en.wikipedia.org/wiki/Solid_of_revolution

    "Cylinder method"

    Granted it's not taught on the A level spec.
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    Nuf respec`
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    (Original post by Hasufel)
    Nuf respec`
    This is taught on the spec it's just c4 not c3.

    It's the Pi*Intergral of y^2 dx

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