/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q10P Evaluate each of the following i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q10P (page 314)

Evaluate each of the following integrals in the easiest way you can.

鈭�(2ydx=3xdy)around the square bounded by x=3, x=5, y=1 and y=3

Short Answer

Expert verified

The solution to this problem is /=-20

Step by step solution

01

Given Information.

The given information is鈭�(2ydx=3xdy)

02

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.

03

Find the solution.

Write the values of P and Q.

P=2y

Q=-3x

Find the difference of their differentiation

鈭�Q鈭�X-鈭�P鈭�y=-3-2=-5

The integral is in the form mentioned below.

/=-5鈭�13鈭�35dxdy=-5脳4=-20

Hence, the solution to this problem is /=-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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

鈭�V脳苍诲蟽over the entire surface of the sphere, iflocalid="1657353129148" (x鈭�2)2+(y+3)2+(z)2=9, ifV=(3x鈭�yz)i+(z2鈭�y2)j+(2yz+x2)k

Write out the equations corresponding to (9.3) and (9.4) for Q=2Xbetween points 3 and 4 in Figure 9.2, and add them to get (9.6).

Given 蠒=z2-3xy find

(a) grad role="math" localid="1659325059343" 蠒;

(b) The directional derivative of 蠒at the point role="math" localid="1659325089841" (1,2,3) in the directionrole="math" localid="1659325033087" i+j+k;

(c) The equations of the tangent plane and of the normal line to 蠒=3 at the point (1,2,3)

Given

F1=-2yi+(z-2x)j+(y+z)kF2=yi+2xj:

(a) Is F1conservative? Is F2conservative?

(b) Find the work done by 2 on a particle that moves around the ellipse x=cos胃, y=2蝉颈苍胃from 胃=0to胃=2蟺

(c) For any conservative force in this problem find a potential function Vsuch

that F=-鈭�V (d) Find the work done by on a particle that moves along the straight line from (0,1,0)to(0,2,5)

(e) Use Green鈥檚 theorem and the result of Problem 9.7 to do Part (b) above.

鈭�(yi鈭�xj+zk)鈭�draround the circumference of the circle of radius 2, center at the origin, in the (x,y)plane.
See all solutions

Recommended explanations on Physics Textbooks

Space Physics

Read Explanation

Engineering Physics

Read Explanation

Atoms and Radioactivity

Read Explanation

Electricity

Read Explanation

Waves Physics

Read Explanation

Particle Model of Matter

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.