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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: 6,821 Thanks: 723 You need to clarify the area(s?) of interest. As four separate questions, they areas are all infinite. Thanks from Simen Qvam 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
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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

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

$\displaystyle A = \int_a^b e^9 x - \dfrac{5}{x} \, dx + \int_b^c \dfrac{10}{x} - \dfrac{5}{x} \, dx + \int_c^d \dfrac{10}{x} -ex \, dx$ 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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post John Travolski Advanced Statistics 3 October 30th, 2017 06:06 PM zollen Calculus 4 October 18th, 2017 06:08 AM hellowz Algebra 3 July 4th, 2013 08:26 PM rowdy3 Calculus 6 May 5th, 2010 04:12 AM shalinisharma512 Algebra 1 April 7th, 2009 02:21 AM

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