   Chapter 16, Problem 3RE

Chapter
Section
Textbook Problem

Evaluate the line integral.3. ∫C yz cos x ds, C: x = t, y = 3 cos t, z = 3 sin t, 0 ⩽ t ⩽ π

To determine

To Evaluate: The line integral Cyzcosxds C:x=t,y=3cost,z=3sint,0tπ .

Explanation

Given data:

The parametric equations of curve and its limits are given as follows.

C:x=t,y=3cost,z=3sint,0tπ

Formula used:

Write the expression to evaluate the line integral for a function f(x,y) along the curve C .

Cf(x,y)ds=abf(x(t),y(t))(dxdt)2+(dydt)2dt (1)

Here,

a is the lower limit of the curve C and

b is the upper limit of the curve C .

Write the required differential and integration formulae to evaluate the given integral.

ddxcosx=sinxddxsinx=cosx[f(x)]ndx=[f(x)]n+1n+1

Modify equation (1) as follows.

Cf(x,y)ds=abf(x,y)(dxdt)2+(dydt)2+(dzdt)2dt

Substitute yzcosx for f(x,y) , t for x , 3cost for y , 3sint for z , 0 for a , and π for b ,

Cyzcosxds=0π(3cost)(3sint)(cost)(ddt(t))2+(ddt(3cost))2+(ddt(3sint))2dt=0π(9cos2tsint)(1)2+(3sint)2+(3cost)2dt=0π(9cos2tsint)1+9sin2t+9cos2tdt=0π(9cos2tsint)1+9(sin2t+cos2t)dt

Rewrite the equation as follows

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find the derivative of the function. y=(x+1x)5

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 2528. solve the equation by factoring. 28. 2x4 + x2 = 1

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

If n is a positive integer, prove that 01(lnx)ndx=(1)nn!

Single Variable Calculus: Early Transcendentals

Show that modus tollens is a valid form of argument.

Finite Mathematics for the Managerial, Life, and Social Sciences 