October 5th, 2017, 07:11 AM  #1 
Senior Member Joined: Jan 2017 From: Toronto Posts: 178 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: 384 Thanks: 208 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: 3,198 Thanks: 872 
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 $\displaystyle \frac{1}{x}$! 

Tags 
integral, line, problem, vector 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Evaluate the line integral vector filed (curve)  xl5899  Calculus  18  January 2nd, 2017 08:22 AM 
3d Line integral problem  max233  Calculus  2  May 22nd, 2016 04:37 AM 
Line integral of solenoidal vector field  neelmodi  Calculus  1  March 11th, 2015 05:17 AM 
Line integral of vector field  physicsstudent  Calculus  1  June 6th, 2014 08:16 PM 
Very simple line integral problem  too_old  Calculus  0  November 30th, 2008 02:08 PM 