please assist with first question 1. Use Stokes'theorem to evaluate F. dr where F = z²i + y² + xk and C is the triangleсwith vertices (1,0,0), (0,1,0) and (0,0,1) with anticlockwise rotation.2. Evaluate the following line integral using Green's theoremy²dx + x²dy,Cwhere C is the square with vertices (0, 0), (1, 1), (0, 1) oriented counter clockwise.3. Use the Divergence theorem to find the flux ofF(x, y, z) = xi + y) + zkacross the surface o with outward orientation, which is the surface of the solid boundedby the paraboloid z = √1-x² - y² and the xy-plane

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Answered: 1. Use Stokes'theorem to evaluate fF.dr…

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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.5: Polar Coordinates

Problem 97E

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Question

please assist with first question

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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