Answered: Let H be the segment of the hyperbola…

Let H be the segment of the hyperbola x-y°= | Connecting (1,0) to (2, J3). Evaluate the line, integral %3D Suly dx t x dy

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.3: Hyperbolas

Problem 25E

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Question

Let H be the segment of the hyperbola xy°= |
Connecting (1,0) to (2, J3). Evaluate the line inegral.
Suly
+) dx + x dy
メ

Expert Solution

Step 1

Given

H be the segment of hyperbola $x^{2} - y^{2} = 1$ connecting the points (1,0) to (2, $\sqrt{3}$ )

we have to evaluate the integral

$\int_{H} (y + \frac{1}{x}) d x + x d y$

Now by using Green's theorem we know that

$\int_{c} M d x + N d y = \iint_{s} (\frac{\partial N}{\partial x} - \frac{\partial M}{\partial y}) d x d y$

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