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March 5th, 2019, 08:31 AM  #1 
Newbie Joined: Mar 2019 From: Norway Posts: 3 Thanks: 0  Using substitution of variables to find area
Find the area in the first quadrant limite by the curves xy=5, xy=10, y=ex and y=(e^9)x The answer should be an exact rational number. ps: You are expected to substitute variables 
March 5th, 2019, 01:02 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,704 Thanks: 670 
You need to clarify the area(s?) of interest. As four separate questions, they areas are all infinite.

March 5th, 2019, 01:20 PM  #3 
Newbie Joined: Mar 2019 From: Norway Posts: 3 Thanks: 0 
It should be the area between all of these curves, if that makes sense

March 5th, 2019, 01:21 PM  #4  
Math Team Joined: Jul 2011 From: Texas Posts: 2,838 Thanks: 1481  Quote:
$a = \sqrt{\dfrac{5}{e^9}}$ $b = \sqrt{\dfrac{10}{e^9}}$ $c = \sqrt{\dfrac{5}{e}}$ $d = \sqrt{\dfrac{10}{e}}$ $\displaystyle A = \int_a^b e^9 x  \dfrac{5}{x} \, dx + \int_b^c \dfrac{10}{x}  \dfrac{5}{x} \, dx + \int_c^d \dfrac{10}{x} ex \, dx$  
March 5th, 2019, 04:47 PM  #5 
Newbie Joined: Mar 2019 From: Norway Posts: 3 Thanks: 0 
This is my first question on this forum, so i might not have stated the question in the right manner. I have tried selecting u = xy and v = y/x. Which would the area a rectangle from u=5 to u=10 and v = e to v =e^9. But when i try to compute the jacobian determinant i am stuck, i end up with a term that i do not know what to do with, as it is not a just a number... Thank you guys for the help so far, just ask for any clarification! 

Tags 
area, find, multivariable calculus, substitution, variables 
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