October 5th, 2017, 07:11 AM  #1 
Senior Member Joined: Jan 2017 From: Toronto Posts: 190 Thanks: 2  Vector Line Integral problem
Evaluate the line integral: $\displaystyle \int_{C}^{} y ~dx  x ~dy $ where C is the portion of the curve y= 1/x from (1,1) to (2, 1/2). My answer: 2 ln(2) = $\displaystyle \int_{1}^{2} (1/t, t) ~*~ (1, 1/t^2) ~dt = \int_{1}^{2} 2/t ~dt $ Official Answer: Log(4) Last edited by zollen; October 5th, 2017 at 07:15 AM. 
October 5th, 2017, 08:16 AM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 444 Thanks: 254 Math Focus: Dynamical systems, analytic function theory, numerics 
These are the same answer. $2 \ln(2) = \ln(2^2) = \ln 4$.

October 5th, 2017, 08:19 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
Okay, do you have a question? You wound up with $\displaystyle 2\int_1^2 \frac{1}{t}dt$. Are you saying you no know how to integrate $\displaystyle \int \frac{1}{t}dt$? Hint: the derivative of ln(x) is $\displaystyle \frac{1}{x}$! 

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integral, line, problem, vector 
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