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October 5th, 2017, 07:11 AM   #1
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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.
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October 5th, 2017, 08:16 AM   #2
SDK
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These are the same answer. $2 \ln(2) = \ln(2^2) = \ln 4$.
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October 5th, 2017, 08:19 AM   #3
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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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