Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
with f an integrable function in R, where R is the region of the XY plane represented in the graph: z+y = 1 2 + y² = 1 R

with f an integrable function in R, where R is the region of the XY plane represented in the graph: z+y = 1 2 + y² = 1 R

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

Considere la integral doble: (see attached image)

When transforming the previous integral applying the change of variable to polar coordinates, we obtain:

 

f(x, y) dA, x² + y? with f an integrable function in R, where R is the region of the XY plane represented in the graph: x +y = 1 a? + y? = 1 R
Transcribed Image Text:f(x, y) dA, x² + y? with f an integrable function in R, where R is the region of the XY plane represented in the graph: x +y = 1 a? + y? = 1 R
7/2 f(r cos(0), r sen(0)) A) I = drde r2 /1-r cos(0) /2 f(r cos(0), r sen(0)) drd0 B) I = 1 cos (0)+sen(8) 7/2 C) I = ["L f(r cos(0), r sen(0)) drd0 r2 cos (0)+sen(8) f(r cos(0), r sen(0)) drd0 D) I = 0. 1-r cos(0)
Transcribed Image Text:7/2 f(r cos(0), r sen(0)) A) I = drde r2 /1-r cos(0) /2 f(r cos(0), r sen(0)) drd0 B) I = 1 cos (0)+sen(8) 7/2 C) I = ["L f(r cos(0), r sen(0)) drd0 r2 cos (0)+sen(8) f(r cos(0), r sen(0)) drd0 D) I = 0. 1-r cos(0)
Expert Solution
Step 1

Given: f is an Integrable function in R

where R is the region of the XY plane.

We have to change the variable of ∬Rfx,yx2+y2dA

Substitute x=rcosθ, y=rsinθ

we get x2+y2=r2

 

 

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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,
SEE MORE TEXTBOOKS