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Intersection for integration

  1. Sep 14, 2013 #1
    1. The problem statement, all variables and given/known data

    Hi I'm trying to find where these two graphs intersect I would like it to be exact but it isn't quite working.
    If I have y = tan(x) and y = x^1/3 how can I solve exactly?
    2. Relevant equations

    tan(x) = x^1/3 ??? Hmm.
    I'm not sure. I don't want arctan popping up on the right side. So I don't know really.

    3. The attempt at a solution
     
  2. jcsd
  3. Sep 14, 2013 #2

    Ray Vickson

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    Show your work.
     
  4. Sep 14, 2013 #3
    I'm supposed to just set up the integral not evaluate it. They want me to consider y = tanx and y = x^1/3 in the first quadrant.
    Rotated about x I have:
    V = 2PI (integral) x(tanx-x^1/3) dx
    Between what ever result I get for the intersection of 0 and tanx = x^1/3
    and for about y I have
    V = 2PI( integral) y(arctan(y) - y^3) dy
    Between 0 and whatever y^3 = arctan(y) intersections is.
     
  5. Sep 14, 2013 #4
    This is my work
    tan(x) = x^1/3
    x = arctan(x^1/3) ok ..... now i'm stuck
     
  6. Sep 14, 2013 #5

    Ray Vickson

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    That's because there is (very probably) no closed-form solution; just use a numerical method.
     
  7. Sep 15, 2013 #6
    What do you mean a numerical method and how am I supposed to indicate the upper bound my teacher gives 0's for decimals. Also does my integrals look OK?
     
  8. Sep 15, 2013 #7
    Do my integrals look set up properly? Also how am I supposed to write an upper limit? Like integral from 0 to
    tan(x) = x^1/3? Because I can't really solve this but I have to represent it exactly.
     
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