Reverse the order of integration?

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Homework Statement



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?

Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #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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