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
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: Evaluatexy? ds where C is the right half of thecircle x2 + y?4

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

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter11: Rational And Irrational Numbers

Section11.5: Square Roots Of Variable Expressions

Problem 10MRE

See similar textbooks

Related questions

Topic Video

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:

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

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Quadrilaterals$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions