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Calculate the surface integral 1 (V × F) - dS where M is the hemisphere ² + y² + 2² = 9, π ≥ 0, with the normal in the direction of the positive x direction, and F = (0, 0, y¹)). Begin by writing down the "standard" parametrization of OM as a function of the angle (denoted by "t" in your answer), where ǝM denotes the boundary of M: x= , y = 2π Sam F ds = f(0) do, where f(0) = The value of the integral is (use "t" for theta).

Calculate the surface integral 1 (V × F) - dS where M is the hemisphere ² + y² + 2² = 9, π ≥ 0, with the normal in the direction of the positive x direction, and F = (0, 0, y¹)). Begin by writing down the "standard" parametrization of OM as a function of the angle (denoted by "t" in your answer), where ǝM denotes the boundary of M: x= , y = 2π Sam F ds = f(0) do, where f(0) = The value of the integral is (use "t" for theta).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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Calculate the surface integral x √ (V × F) - dS where M is the hemisphere a² + y² + z² = 9, a ≥ 0, with the normal in the direction of the positive x direction, and F = (x, 0, y¹)). Begin by writing down the "standard" parametrization of M as a function of the angle (denoted by "t" in your answer), where ƏM denotes the boundary of M: X , y= ,2= 2πT Sam F. ds = f(0) do, where f(0) = = The value of the integral is (use "t" for theta).
Transcribed Image Text:Calculate the surface integral x √ (V × F) - dS where M is the hemisphere a² + y² + z² = 9, a ≥ 0, with the normal in the direction of the positive x direction, and F = (x, 0, y¹)). Begin by writing down the "standard" parametrization of M as a function of the angle (denoted by "t" in your answer), where ƏM denotes the boundary of M: X , y= ,2= 2πT Sam F. ds = f(0) do, where f(0) = = The value of the integral is (use "t" for theta).
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