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Calculus 2 volume integration, y=axis

  1. Nov 3, 2011 #1
    Hello, so I've been having lots of trouble with a math problem.
    I can differentiate functions but i'm kinda confused on what to do when it is like y=4

    So say you have the given: y= x^2 and then y=4, x=0, x=2. Rotate about the y-axis.
    I'm know you have to get it into respect to y so x=sqrt(y) but what would I do from there?! you can't put x in terms of y for y=4! i'm confused. Can somebody help me out or point me in the right direction.
     
  2. jcsd
  3. Nov 3, 2011 #2

    mathwonk

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    they are giving you 4 different curves or lines and you are supposed to envision the region bounded by those curves or lines. so you have the line y=4 at the top, y=x^2 on the right, .......

    ooops, your equations do not fit together to give one region. you need to re - read the question.
     
  4. Nov 3, 2011 #3
    Okay well the y=x^2 is a parabola so it goes on both sides of the y-axis. And then the y=4 is another bounding line.

    we are supposed to rotate the bounded region from x=0 to 2 around the y-axis.

    I'm just confused on how to rotate it around like that.
     
  5. Nov 3, 2011 #4

    mathwonk

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    well you don't want to say x=2 if you know y=4 and y = x^2. rather you should say y = x^2 for x≥0, y=4, and x=0. but if thats what it said, its their fault not yours.

    so apparently the region is bounded by y = x^2 for x≥0, x = 0 and y=4. that makes it a portion of the right half of the parabola. then you rotate it around the y axis.


    is that hard to see? your book may not be too well written.
     
  6. Nov 3, 2011 #5
    well they give me the limits x=0 and x=2. y=x^2 and y=4 intersect at x=2.

    I can imagine it. I'm just confused how to rotate it around the y=axis. what method to use and how to get the variables needed in the method. I tried the shells method and that didn't work. I didn't understand how to get the needed material.
     
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