/*! 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 16. Evaluate the line integral of th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Q 16. (page 1154)

Evaluate the line integral of the given function over the specified curve.

鈭�CFx,y,z.drwhere Fx,y,z=ex,ey,ezand C is the curve parametrized by x=t,y=t2,z=t3for 0鈮�t鈮�1.

Short Answer

Expert verified

鈭�CFx,y,z.dr=3e

Step by step solution

01

Given Information

The given expression is Fx,y,z=ex,ey,ezandx=t,y=t2,z=t3

02

Simplification

Using the given values of x,y,zin function

Fx,y,z=ex,ey,ez

Differentiating parameters, we get

rt=1,2t,3t2

The line integral is evaluated as

鈭�CF(x,y,z).dr=鈭�01exeyez1,2t,3t2dt

鈭�CF(x,y,z).dr=鈭�01et+2tet2+3t2et3dt

localid="1651521623828" 鈭�CF(x,y,z).dr=et+et2+et301

(This is obtained by solving integration by substitution)

鈭�CF(x,y,z).dr=e+e+e=3e

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

Integrate the given function over the accompanying surface in Exercises 27鈥�34.

f(x,z)=e-(x2+z2), where S is the unit disk centered at the point (0, 2, 0)and in the plane y = 2.

What is the difference between the graphs of

G(x,y)=i+jandF(x,y)=2i+2j

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.

Area: Finding the area of a region in the x y-plane is one of the motivating applications of integration. It is also a special case of the surface area calculation developed in this section. Find the area of the region in the x y-plane bounded by the curvesy=x2andx=y.

Problem Zero: Read the section and make your own summary of the material.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Statistics

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.