Chapter 6: Q9P (page 314)

Evaluate each of the following integrals in the easiest way you can.
$\oint (2 y d x - 3 x d y)$ around the square bounded by $x = 3, x = 5, y = 1 a n d y = 3 .$

Short Answer

Expert verified

The solution to this problem is $I = - 20 .$

Step by step solution

Given Information.

The given information is $\oint (2 y d x - 3 x d y)$

Definition of Green’s Theorem.

The Green's theorem connects a line integral around a simple closed curve C to a double integral over the plane region D circumscribed by C in vector calculus. Stokes' theorem has a two-dimensional special case.

Find the solution.

Write the values of P and Q.

$P = 2 y Q = - 3 x$

Find the difference of their differentiation

$\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} = - 3 - 2 = - 5$

The integral is in the form mentioned below.

$l = - 5 \int_{1}^{3} \int_{3}^{5} d x d y = - 5 \times 4 = - 20$

Hence, the solution to this problem is $l - 20$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Evaluate each of the following integrals in the easiest way you can.
$\oint (2 y d x - 3 x d y)$ around the square bounded by $x = 3, x = 5, y = 1 a n d y = 3 .$

Short Answer

Step by step solution

Given Information.

Definition of Green’s Theorem.

Find the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Scientific Method Physics

Classical Mechanics

Particle Model of Matter

Translational Dynamics

Astrophysics

Space Physics

Study anywhere. Anytime. Across all devices.

Evaluate each of the following integrals in the easiest way you can.∮(2ydx-3xdy)around the square bounded by x=3,x=5,y=1andy=3.

Short Answer

Step by step solution

Given Information.

Definition of Green’s Theorem.

Find the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Scientific Method Physics

Classical Mechanics

Particle Model of Matter

Translational Dynamics

Astrophysics

Space Physics

Study anywhere. Anytime. Across all devices.

Evaluate each of the following integrals in the easiest way you can.
$\oint (2 y d x - 3 x d y)$ around the square bounded by $x = 3, x = 5, y = 1 a n d y = 3 .$