My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Thanks Tree2Thanks
  • 1 Post By mathman
  • 1 Post By skeeter
Reply
 
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
Simen Qvam is offline  
 
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.
Thanks from Simen Qvam
mathman is offline  
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
Simen Qvam is offline  
March 5th, 2019, 01:21 PM   #4
Math Team
 
skeeter's Avatar
 
Joined: Jul 2011
From: Texas

Posts: 3,016
Thanks: 1600

Quote:
Find the area in the first quadrant limite by the curves

xy=5, xy=10, y=ex and y=(e^9)x
recommend you sketch the region in quadrant I

$a = \sqrt{\dfrac{5}{e^9}}$
$b = \sqrt{\dfrac{10}{e^9}}$
$c = \sqrt{\dfrac{5}{e}}$
$d = \sqrt{\dfrac{10}{e}}$

$\displaystyle A = \int_a^b e^9 x - \dfrac{5}{x} \, dx + \int_b^c \dfrac{10}{x} - \dfrac{5}{x} \, dx + \int_c^d \dfrac{10}{x} -ex \, dx$
Thanks from Simen Qvam
skeeter is offline  
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!
Simen Qvam is offline  
Reply

  My Math Forum > College Math Forum > Calculus

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





Copyright © 2019 My Math Forum. All rights reserved.