/*! 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} Q 29. Evaluate each of the vector fiel... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Q 29. (page 1107)

Evaluate each of the vector field line integrals over the indicated curves.

F(x,y)=i-j with C the curve with equationy-x2=1for5鈮�x鈮�10.

Short Answer

Expert verified

The required line integral is-70.

Step by step solution

01

Given Information

It is given that F(x,y)=i-j

The curve is parametrized byy-x2=1for5鈮�x鈮�10

02

Solving the parametric equations

The given curve is parametrize by

x(t)=t,y(t)=1+t2,5鈮�t鈮�10

鈬�x'(t)=1,y'(t)=2t

Hence, C:r(t)=t,1+t2

Also

F(x(t),y(t))=i-j

And r'(t)=x'(t),y'(t)

=(1)i+(2t)j

03

Solving the line integral

The formula for line integral is

鈭�CF路dr=鈭�CF(x(t),y(t))路r'(t)dt

=鈭�510[(1)i+(-1)j]路[(1)i+(2t)j]dt

=鈭�510(1-2t)dt

=t-t2510

=[10-100]-[5-25]

=-90+20

=-70

The line integral is -70.

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

The current through a certain passage of the San Juan Islands in Washington State is given by

F=F1(x,y),F2(x,y)=0,1.152-0.8x2.

Consider a disk R of radius 1 mile and centered on this region. Denote the boundary of the disk by localid="1650455155947" 鈭�R.

  • (a) Compute localid="1650455166518" 鈭�R鈭�F2鈭�x-鈭�F1鈭�ydA.
  • (b) Show that鈭�鈭�RF路nds=鈭�02蟺1.152-0.8cos2胃sin胃d胃. Conclude that Green's Theorem is valid for the current in this area of the San Juan Islands.
  • (c) What do the integrals from Green's Theorem tell us about this region of the San Juan Islands?

Why is dAin Green鈥檚 Theorem replaced by dSin Stokes鈥� Theorem?

What is the difference between the graphs of

G(x,y,z)=-i-j-kandF(x,y,z)=i+j+k

Generalize your answer to Exercise 12 to give a parametrization and a normal vector for the extension of any differentiable plane curve y = f(x) through a 鈮� z 鈮� b.

Fx,y,z=cosxyzi+j-yzk, where S is the portion of the surface with equation z=y3-y2that lies above and/or below the rectangle determined by 鈭�3鈮�x鈮�2and 鈭�1鈮�y鈮�1 in the xy-plane, with n pointing in the positive z direction.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

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.