My Math Forum Using substitution of variables to find area

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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. 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!

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