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Reverse the order of integration?

  1. Mar 20, 2012 #1
    1. The problem statement, all variables and given/known data

    Reverse the order of integration?
    Original has it in the form of dy dx, 0<=x<=ln6, 1<=y<=e^x.
    I made it dx dy, with 1<=x<=e^y, 0<=y<=ln6
    Is this right?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 20, 2012 #2

    HallsofIvy

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    Wow, you waited 12 whole minutes before bumping? That's a good way to get banned from this forum!

    Draw a graph. x ranges between 0 and ln(6) so draw two vertical lines there. For each x[/itex], y ranges from 1 to [itex]y= e^x[/itex] do draw the horizontal line y= 1 and the [itex]y= e^x[/itex]. Notice that [itex]e^0= 1[/itex] so that forms something that looks like a kind of "right triangle" with a curved hypotenuse.

    Now, what are the lowest and highest value of y in that "triangle"? Saying that x< ln 6 does NOT mean y< ln 6. y is not x!
    Imagine a horizontal line at some y-value. x ranges from the left end of that line to the right end. What are those values?

    [itex]y= e^x[/itex] does NOT give [itex]x= e^y[/itex]!! Solve [itex]y= e^x[/itex] for x.
     
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