Evaluatexy? ds where C is the right half of thecircle x2 + y?4

Name: Evaluatexy? ds where C is the right half of thecircle x2 + y?4
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Description: Evaluatexy? ds where C is the right half of thecircle x2 + y?4

Answered: Evaluate xy? ds where C is the right…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 29E

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Question

Evaluate
xy? ds where C is the right half of the
circle x2 + y?
4

Expert Solution

Step 1

C is the right half of the circle: $x^{2} + y^{2} = 4 .$ Therefore use the parametrisation:

$x = 2 \cos t y = 2 \sin t - \frac{π}{2} \leq t \leq \frac{π}{2} \{C is right half of the given circle\}$

Now:

$d s = \sqrt{{(x' (t))}^{2} + {(y' (t))}^{2}} d t d s = \sqrt{{(- 2 \sin t)}^{2} + {(2 \cos t)}^{2}} d t d s = 2 \sqrt{\sin^{2} t + \cos^{2} t} d t d s = 2 d t$

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