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    Hi, I've been working through volumes of revolution and I've got a few questions which I'm unsure about, and just wanted a bit of guidance on them

    1.

    Uploaded with ImageShack.us

    For 4a) Is it sufficient to say that "Even at large values of x, y>0 because it is an asymptote"? I'm not sure how I can 'show' it

    EDIT: I just realised that the attachment is really small. Here's the typed out version: "The diagram shows the curve y=x^-2/3" a) Show that the shaded area A is infinite. (Area A is between x=1 and extends as far as x goes (so infinity))

    2. The part of the graph between y=e^0.5x, the line y=2 and the y axis is rotated about the x-axis to make a solid of revolution. Find the volume of this solid, giving your answer in the form pi(aln(b) - c)

    So firstly, I needed to find the x value when y=2. So 2=e^0.5x

    ln2 = 0.5x. So x = 2ln2

    And I needed y^2, so (e^0.5x)^2 = e^x.

    Then pi integral 2ln2 and 0 (e^x) dx

    [e^x] 2ln2 and 0

    So e^2ln2 - 1

    So e^ln4 - 1

    =4-1 = 3

    Where have I made a mistake?

    Thanks
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    The image is too small to read.
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    this may be useful:

    http://answers.yahoo.com/question/in...3050032AA4Eg73

    although there are problems with the image here also...
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    (Original post by Mr M)
    The image is too small to read.
    I've just solved the question regarding the image, however like I asked the bear, I wasn't sure what is the best way of explaining that inserting infinity into [3x^1/3] gives infinity.

    Would you be able to help with the second question?

    (Original post by the bear)
    this may be useful:

    http://answers.yahoo.com/question/in...3050032AA4Eg73

    although there are problems with the image here also...
    Thanks, I didn't realise that through integrating it, you'd be able to show that it tends to infinity. You end up with [3x^1/3] infinity and 1

    What is the best way to phrase that if you plug in infinity, then the number will get infinitely big? (Or is that okay?)
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    (Original post by StaedtlerNoris)
    I've just solved the question regarding the image, however like I asked the bear, I wasn't sure what is the best way of explaining that inserting infinity into [3x^1/3] gives infinity.

    Would you be able to help with the second question?



    Thanks, I didn't realise that through integrating it, you'd be able to show that it tends to infinity. You end up with [3x^1/3] infinity and 1

    What is the best way to phrase that if you plug in infinity, then the number will get infinitely big? (Or is that okay?)
    just say that the result is infinitely big
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    (Original post by the bear)
    just say that the result is infinitely big
    Thanks, would you be able to take a look at my working for the second question?
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    (Original post by StaedtlerNoris)
    Thanks, would you be able to take a look at my working for the second question?
    If you were to show that there was an asymptote on the x-axis, that would do. I personally would do this by substuting 0 for y in the equation, you shouldn't be able to do this.. I've never seen that kind of question on a C3 paper, but I'm talking about OCR so it might depend on the exam board. I might be completely wrong here.

    Could you type out the equation, because I can't see it, and I'm able to help you with your working for the next question if you like.
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    (Original post by Pride)
    If you were to show that there was an asymptote on the x-axis, that would do. I personally would do this by substuting 0 for y in the equation, you shouldn't be able to do this.. I've never seen that kind of question on a C3 paper, but I'm talking about OCR so it might depend on the exam board. I might be completely wrong here.

    Could you type out the equation, because I can't see it, and I'm able to help you with your working for the next question if you like.
    Ah okay, I'm on OCR as well Type out the equation for what, the first or the second one? The first one is :y=x^-2/3 the second is included in the question. I followed that link to yahoo answers, and it said that you integrate it, then set the limits as infinity and 1, and that shows that it tends to infinity.

    If you could help with the next question, it would be great.
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    (Original post by StaedtlerNoris)
    Ah okay, I'm on OCR as well Type out the equation for what, the first or the second one? The first one is :y=x^-2/3 the second is included in the question. I followed that link to yahoo answers, and it said that you integrate it, then set the limits as infinity and 1, and that shows that it tends to infinity.

    If you could help with the next question, it would be great.
    Oh ok, so because you're doing OCR, I wouldn't worry about the first question, it won't come up on the exam.

    b) so you'd do the integral limits 0 and 1 takeaway the area of the white square  \int^1_0 x^{-\frac{2}{3}} dx - 1

    have you done that?
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    (Original post by Pride)
    Oh ok, so because you're doing OCR, I wouldn't worry about the first question, it won't come up on the exam.

    b) so you'd do the integral limits 0 and 1 takeaway the area of the white square  \int^1_0 x^{-\frac{2}{3}} dx - 1

    have you done that?
    Er I think we're talking about 2 different questions Are you talking about this one? :
    2. The part of the graph between y=e^0.5x, the line y=2 and the y axis is rotated about the x-axis to make a solid of revolution. Find the volume of this solid, giving your answer in the form pi(aln(b) - c)
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    (Original post by Pride)
    Oh ok, so because you're doing OCR, I wouldn't worry about the first question, it won't come up on the exam.

    b) so you'd do the integral limits 0 and 1 takeaway the area of the white square  \int^1_0 x^{-\frac{2}{3}} dx - 1

    have you done that?
    Hi again, I'm a little bit confused. Under the "Who quoted me" it says that you quoted me in this thread 15 minutes ago, but I was the last poster?
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    (Original post by StaedtlerNoris)
    Hi again, I'm a little bit confused. Under the "Who quoted me" it says that you quoted me in this thread 15 minutes ago, but I was the last poster?
    I deleted a post where I quoted you, I made a mistake
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    (Original post by StaedtlerNoris)
    Er I think we're talking about 2 different questions Are you talking about this one? :
    2. The part of the graph between y=e^0.5x, the line y=2 and the y axis is rotated about the x-axis to make a solid of revolution. Find the volume of this solid, giving your answer in the form pi(aln(b) - c)
    Oh lol, I was looking at 1b hehe
    I'll have to get a pen out

    ok, so here's my working out. First I worked out where the line y = 2 and the curve meet, to find the limits.
    

2 = e^{\frac{1}{2}x}

\dfrac{1}{2}x = ln2

x = ln4



\pi (\int^{ln4}_0 4 dx - \int^{ln4}_0 (e^{\frac{1}{2}x})^2 dx)

\pi (\left[ 4x \right]^{ln4}_0 - \left[ e^x \right]^{ln4}_0)

\pi ((4ln4 - 0) - (e^{ln4} - 1))

\pi (4ln4 - 4 + 1)

\pi (4ln4 - 3)
    that took too long to type out..
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    (Original post by Pride)
    Oh lol, I was looking at 1b hehe
    I'll have to get a pen out

    ok, so here's my working out. First I worked out where the line y = 2 and the curve meet, to find the limits.
    

2 = e^{\frac{1}{2}x}

\dfrac{1}{2}x = ln2

x = ln4



\pi (\int^{ln2}_0 4 dx - \int^{ln2}_0 (e^{\frac{1}{2}x})^2)

\int^2_0 \pi (e^x) dx

\pi (\left[ 4x \right]^{ln2}_0 - \left[ e^x \right]^{ln2}_0

\pi ((4ln4 - 0) - (e^{ln4} - 1))

\pi (4ln4 - 4 - 1)

\pi (4ln4 - 5)
    that took too long to type out...
    I have a few questions, firstly, you found that x = ln4. Should the limits for the integral be ln4 then? And why are you doing the integral of e^0.5x and then subtracting y=2? Isn't y=2 just a boundary? (It's probably unclear what I'm saying, but you have [4x] and [e^x] however I don't see why you used two integrals?)

    Also, the answer is pi(8ln2 - 3)
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    (Original post by StaedtlerNoris)
    I have a few questions, firstly, you found that x = ln4. Should the limits for the integral be ln4 then? And why are you doing the integral of e^0.5x and then subtracting y=2? Isn't y=2 just a boundary? (It's probably unclear what I'm saying, but you have [4x] and [e^x] however I don't see why you used two integrals?)

    Also, the answer is pi(8ln2 - 3)
    oh no, ok let me have another look through

    edit: oh I see, have a look at my post again. btw, 4ln4 is the same as 8ln2
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    (Original post by Pride)
    oh no, ok let me have another look through
    Okay thanks How's your revision going, have you started papers yet?
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    (Original post by StaedtlerNoris)
    Okay thanks How's your revision going, have you started papers yet?
    of course I've started papers lol! of course, that is the best revision for maths C3.

    I have all of the papers except the 2011 and 2012 ones and solutions on fronter, so I've been working my way back from 2010. I've been focusing on my other subjects though, they're sooner.
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    (Original post by StaedtlerNoris)
    I have a few questions, firstly, you found that x = ln4. Should the limits for the integral be ln4 then? And why are you doing the integral of e^0.5x and then subtracting y=2? Isn't y=2 just a boundary? (It's probably unclear what I'm saying, but you have [4x] and [e^x] however I don't see why you used two integrals?)

    Also, the answer is pi(8ln2 - 3)
    Y = 2 is a horizontal line, so you have to find the volume that makes and takeaway the volume y = e^0.5x makes
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    (Original post by Pride)
    of course I've started papers lol! of course, that is the best revision for maths C3.

    I have all of the papers except the 2011 and 2012 ones and solutions on fronter, so I've been working my way back from 2010. I've been focusing on my other subjects though, they're sooner.
    Oh, maybe it's just me who leaves papers late Planning on starting tomorrow. I've just been going through the textbook

    I've done no mechanics...I'm starting to get worried. But I've got Biology/chemistry in about a week's time, so revising those first

    (Original post by Pride)
    Y = 2 is a horizontal line, so you have to find the volume that makes and takeaway the volume y = e^0.5x makes
    ah yes, I've been thinking that it was x = 2. I'm going to redo the question
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    (Original post by Pride)
    Y = 2 is a horizontal line, so you have to find the volume that makes and takeaway the volume y = e^0.5x makes
    Thanks for your help, I've finally got it I made the mistake that e^0 = 0. So I was missing a 1, and I didn't want to look at your working out as it's 'cheating'

 
 
 
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