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Find volume using integrals

  1. Jun 13, 2010 #1
    find volume that is under z = 4x and over area D that is being blocked by y=x^2 y=0 and x=1

    for y = 0 x must be 0 because y = x^2

    so x will go from 0 to 1

    y will go from 0 to x^2

    but what about z? Will it go from 0 to 4x or should I say

    z = 4x
    y = x^2

    that means y = z^2/16 => z = +/-4y

    so z will be from -4y to 4y

    here are the integrals

    [PLAIN]http://www4a.wolframalpha.com/Calculate/MSP/MSP78419b3422a5ih9i1h4000014hgdh31a28gi7dh?MSPStoreType=image/gif&s=52&w=206&h=42 [Broken]

    or

    [PLAIN]http://www4a.wolframalpha.com/Calculate/MSP/MSP82019b343dd21edg47g00000i387ecif97gh4gf?MSPStoreType=image/gif&s=43&w=182&h=39 [Broken]

    thanks in advance
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jun 13, 2010 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The first form is incorrect. y is not equal to [itex]x^2[/itex] throughout the region, only at the top boundary. z=4x on the entire region so the second integral is correct.
     
  4. Jun 13, 2010 #3
    thank you again i dont know what happened to the pictures, they suddenly dissapeared (wolfram alpha deleted them too)

    thanks
     
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