Problem. Use the spherical coordinatas, I= psin o cos 0, y= psin osin 0, z= pcos o; p = r +y° +z, dV = p° sin o dp dộ do, to calculate the intogral I. "av, where E is the solid hemisphere r? + y? + z <1, z 2 0. SII,-av. dV,
Problem. Use the spherical coordinatas, I= psin o cos 0, y= psin osin 0, z= pcos o; p = r +y° +z, dV = p° sin o dp dộ do, to calculate the intogral I. "av, where E is the solid hemisphere r? + y? + z <1, z 2 0. SII,-av. dV,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%

Transcribed Image Text:Problem. Use the spherical coordinatas,
I= psin o cos 0, y= psin osin 0, z= pcos o;
p = r +y° +z, dV = p° sin o dp dộ do,
to calculate the intogral
I. "av,
where E is the solid hemisphere r? + y? + z <1, z 2 0.
SII,-av.
dV,
Expert Solution

Step 1
Let us first analyse E to get the limit values of integration.
We are given that E is the solid hemisphere x2+y2+z2 ≤ 1 and z ≥ 0.
This hemisphere is centered at the origin and is considered only in the positive direction of z.
We have taken,
So, by the above conditions, the region of integration E in spherical coordinates is described by the inequalities
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 4 images

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,

