4. Evaluate √3x²e¹² da + 2x¹yev dy where the open curve C is the semicircle x² + y² = 5, y ≥ 0 going in counterclockwise direction.
4. Evaluate √3x²e¹² da + 2x¹yev dy where the open curve C is the semicircle x² + y² = 5, y ≥ 0 going in counterclockwise direction.
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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Question

Transcribed Image Text:4.
Evaluate
√3x³e³dz +2r³ye dy
where the open curve C is the semicircle x² + y²
=
5, y 0 going in counterclockwise
direction.
5.
Use Stokes theorem to evaluate
1/₁
V x F. dS
over the surface of the paraboloid z = 5 - x² - y² above the plane z = 1, where
F = = (y − 3z) i + (x² − 4z)j + (x + 3y) k
Hint: Stokes' theorem ffsVX FdS=fFdR. What is C in this case?
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