Evaluate the integral of the function f(x, y) = 4 along the circle of radius 2 oriented clock-wise whose parametrization is given by r(t) = (2 cos 0, 2 sin 0), 0 E [0, 27] (2 decimals is ok) Type your answer.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Evaluate the integral of the function f (x, y) = 4 along the circle of radius 2 oriented clock-wise whose parametrization is given by
r(t) = (2 cos 0, 2 sin 0), 0 E [0, 27]
(2 decimals is ok)
Type your answer.
Transcribed Image Text:Evaluate the integral of the function f (x, y) = 4 along the circle of radius 2 oriented clock-wise whose parametrization is given by r(t) = (2 cos 0, 2 sin 0), 0 E [0, 27] (2 decimals is ok) Type your answer.
Expert Solution
Step 1

Given that f(x,y)=4 along the circle of radius 2 oriented clock wise whose parametrization is given by r(t)=2cosθ,2sinθ, θ0,2π.

The objective is to find the integral for the function.

So Cf(x,y)dS

Now the integral can be rewritten as,

I=02πf(r(θ)).r'(θ)dθ

It is given that 

f(x,y)=4f(r(t))=4

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Double Integration
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,