
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 6,821 Thanks: 723 
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: 3,016 Thanks: 1600  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 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Find Joint PDF of two Random Variables  John Travolski  Advanced Statistics  3  October 30th, 2017 06:06 PM 
Defining boundaries with substitution of variables  zollen  Calculus  4  October 18th, 2017 06:08 AM 
Trying to find Ratio between two Variables  hellowz  Algebra  3  July 4th, 2013 08:26 PM 
Find the limit by direct substitution.  rowdy3  Calculus  6  May 5th, 2010 04:12 AM 
Find minimum value of these three variables  shalinisharma512  Algebra  1  April 7th, 2009 02:21 AM 