Let R:x²

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 27E: Let x and y be in Z, not both zero, then x2+y2Z+.
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Let R:x²<ys
3
be the closed region having boundary C with counter-clockwise orientation. F=[X cosh3y, x sinh3y]. Using Green's theorem,
evaluate the line integral P. dr and answer the following questions.
Transcribed Image Text:Let R:x²<ys 3 be the closed region having boundary C with counter-clockwise orientation. F=[X cosh3y, x sinh3y]. Using Green's theorem, evaluate the line integral P. dr and answer the following questions.
Expert Solution
Step 1

We are given that the closed region R: x2 ≤ y ≤ x/3, is having boundary C with counter-clockwise orientation.

The closed region looks like,

                                    Advanced Math homework question answer, step 1, image 1.

And the intersecting points y = x2 and y = x/3 are,

                                     Advanced Math homework question answer, step 1, image 2.

Step 2

For (2),

So, we have x2 ≤ y ≤ x/3 and 0 ≤ x ≤ 1/3.

Answer: 

Advanced Math homework question answer, step 2, image 1

Step 3

We have F = [x cosh(3y), x2 sinh(3y)].

Advanced Math homework question answer, step 3, image 1

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