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1. Use Stokes'theorem to evaluate fF.dr where F = z²î + y² + xk and C is the triangle C with vertices (1,0,0), (0,1,0) and (0,0,1) with anticlockwise rotation.

1. Use Stokes'theorem to evaluate fF.dr where F = z²î + y² + xk and C is the triangle C with vertices (1,0,0), (0,1,0) and (0,0,1) with anticlockwise rotation.

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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1. Use Stokes'theorem to evaluate F. dr where F = z²i + y² + xk and C is the triangle с with vertices (1,0,0), (0,1,0) and (0,0,1) with anticlockwise rotation. 2. Evaluate the following line integral using Green's theorem y²dx + x²dy, C where C is the square with vertices (0, 0), (1, 1), (0, 1) oriented counter clockwise. 3. Use the Divergence theorem to find the flux of F(x, y, z) = xi + y) + zk across the surface o with outward orientation, which is the surface of the solid bounded by the paraboloid z = √1-x² - y² and the xy-plane
Transcribed Image Text:1. Use Stokes'theorem to evaluate F. dr where F = z²i + y² + xk and C is the triangle с with vertices (1,0,0), (0,1,0) and (0,0,1) with anticlockwise rotation. 2. Evaluate the following line integral using Green's theorem y²dx + x²dy, C where C is the square with vertices (0, 0), (1, 1), (0, 1) oriented counter clockwise. 3. Use the Divergence theorem to find the flux of F(x, y, z) = xi + y) + zk across the surface o with outward orientation, which is the surface of the solid bounded by the paraboloid z = √1-x² - y² and the xy-plane
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