I need to solve whole question Let R:x²

Name: I need to solve whole question Let R:x²
Uploaded: 2024-03-20T07:07:37.000Z
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Description: I need to solve whole question Let R:x²

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

Answered: Let R:x²

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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I need to solve whole question

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,

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

Step 2

For (2),

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

Answer:

Step 3

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

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