Let's look at the level area (draw a picture!)D = {(x, y) = R²|0 ≤ x ≤ 2, 0 ≤ y ≤4-x²}and the vector field F(x, y) = -5xy i+ 3x j.a) Calculate the plane integral appearing in Green's formula(OF₂_OF₁)(OF2F1дуb) Calculate the line integral of Green's formula11.dA.f F₁ dx + F₂ dyƏDand state equality with point a.Hint: In this type of line integrals, it is often useful to check if some part of the edge has F1 dx = 0or F2 dy = 0, in which case the parameterizations of these parts do not have to be written at all.(The sum of the digits in the answer is 9.)

Answered: Image /qna-images/answer/ca30bea8-cfcc-48a3-a83a-f45c813ce2a0.jpg

Let's look at the level area (draw a picture!) D = {(x, y) = R² | 0 ≤ x ≤ 2, 0 ≤ y ≤ 4− x²} and the vector field F(x, y) = -5xy i+ 3xj. a) Calculate the plane integral appearing in Green's formula II. (OF-OF) ду b) Calculate the line integral of Green's formula f F₁ dx + F₂ dy dA. and state equality with point a. Hint: In this type of line integrals, it is often useful to check if some part of the edge has F1 dx = 0 or F2 dy = 0, in which case the parameterizations of these parts do not have to be written at all. (The sum of the digits in the answer is 9.)

Let's look at the level area (draw a picture!) D = {(x, y) = R² | 0 ≤ x ≤ 2, 0 ≤ y ≤ 4− x²} and the vector field F(x, y) = -5xy i+ 3xj. a) Calculate the plane integral appearing in Green's formula II. (OF-OF) ду b) Calculate the line integral of Green's formula f F₁ dx + F₂ dy dA. and state equality with point a. Hint: In this type of line integrals, it is often useful to check if some part of the edge has F1 dx = 0 or F2 dy = 0, in which case the parameterizations of these parts do not have to be written at all. (The sum of the digits in the answer is 9.)

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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Question

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Let's look at the level area (draw a picture!)
D = {(x, y) = R²|0 ≤ x ≤ 2, 0 ≤ y ≤4-x²}
and the vector field F(x, y) = -5xy i+ 3x j.
a) Calculate the plane integral appearing in Green's formula
(OF₂_OF₁)
(OF
2F1
ду
b) Calculate the line integral of Green's formula
11.
dA.
f F₁ dx + F₂ dy
ƏD
and state equality with point a.
Hint: In this type of line integrals, it is often useful to check if some part of the edge has F1 dx = 0
or F2 dy = 0, in which case the parameterizations of these parts do not have to be written at all.
(The sum of the digits in the answer is 9.)

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Hi there is a follow up question here. It just changes the parameters in the previous question. I will give "like" immediately when the answer is ready

Repeat the previous question invoices to the vector field f (x, y) = -5yi
+ 5xj tire range
{(x, y) = R² | 4 ≤ x² + y² ≤ 9}.
Tip: Draw the pattern and mark the positive directions of the edge
R
-
curves.

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