(b) Verify Stokes' theorem on a region which is a portion of the sphere x? +y? +z² = 16 which lies above the plane z 2 and with F(x, Y, z) = x²i – z²j + yzk.
(b) Verify Stokes' theorem on a region which is a portion of the sphere x? +y? +z² = 16 which lies above the plane z 2 and with F(x, Y, z) = x²i – z²j + yzk.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please do b) only
Transcribed Image Text:(b) Verify Stokes' theorem on a region which is a portion of the sphere x2 +y?+2 :
16 which lies above the plane z
2 and with F(x, Y, z) = x²i – 2²j + yzk.
(c) Suppose that o is differentiable. Prove the identity
$V¢ •nds
= ,(v*o + V¢ • V¢) dA
D
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