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Evaluate the integral

Evaluate the integral

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
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I need help with a problem using stokes theorem and divergence theorem

Evaluate the integral I = = xz° dydz + dzdx around the closed area A defined by the hemisphere z y a-x-y and the plane z 0. (Hint: Recall that, when we wanted to evaluate a general surface integral, we wrote dA'= dA cos y = dxdy, which was just the projection of dA onto the x-y plane. Show that you can also express this in the form dA'= dxdy =2 n dA, where n is the outward unit normal vector to the surface element dA. Similarly, show that dydz dA cos a = ndA, etc.) %3D %3!
Transcribed Image Text:Evaluate the integral I = = xz° dydz + dzdx around the closed area A defined by the hemisphere z y a-x-y and the plane z 0. (Hint: Recall that, when we wanted to evaluate a general surface integral, we wrote dA'= dA cos y = dxdy, which was just the projection of dA onto the x-y plane. Show that you can also express this in the form dA'= dxdy =2 n dA, where n is the outward unit normal vector to the surface element dA. Similarly, show that dydz dA cos a = ndA, etc.) %3D %3!
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