curl(F) N dS, where (x, y, 2) = -y(a² + y³)2021 î + In(z +1)e*y² }+ z2021 V²+ y? k and S is the portion of the surface z = x? +y² lying below the plane z = 1, oriented dowmward. (Hint: Do NOT try to compute the integral directly. Use Stokes theorem!)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Compute the integral 

·Ñ dS,
where
F (x, y, 2) = -y(x²+ y³)2021 ¿ + In(z + 1)e³*y² j + z²
2021 12 + y² k&
and S is the portion of the surface z = x? + y² lying below the plane z = 1, oriented downward. (Hint: Do NOT try
to compute the integral directly. Use Stokes theorem!)
Transcribed Image Text:·Ñ dS, where F (x, y, 2) = -y(x²+ y³)2021 ¿ + In(z + 1)e³*y² j + z² 2021 12 + y² k& and S is the portion of the surface z = x? + y² lying below the plane z = 1, oriented downward. (Hint: Do NOT try to compute the integral directly. Use Stokes theorem!)
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