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Verify Stokes' theorem for the helicoid Y(r, 0) = (r cos 0, r sin 0, 0) where (r, 0) lies in the rectangle [0, 1] × [0, л/2], and F is the vector field F = (7z, 8x, 4y). First, compute the surface integral: (V × F) · dS = få ſå ƒ(r, 0)dr d0, where a = b = f(r, 0) = Finally, the value of the surface integral is , C = g(0) = Next compute the line integral on that part of the boundary from (1, 0, 0) to (0, 1, л/2). ScF. dr = = g(0) do, where a = ,b= d = (use "t" for theta). and (use "t" for theta). , and

Verify Stokes' theorem for the helicoid Y(r, 0) = (r cos 0, r sin 0, 0) where (r, 0) lies in the rectangle [0, 1] × [0, л/2], and F is the vector field F = (7z, 8x, 4y). First, compute the surface integral: (V × F) · dS = få ſå ƒ(r, 0)dr d0, where a = b = f(r, 0) = Finally, the value of the surface integral is , C = g(0) = Next compute the line integral on that part of the boundary from (1, 0, 0) to (0, 1, л/2). ScF. dr = = g(0) do, where a = ,b= d = (use "t" for theta). and (use "t" for theta). , and

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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Verify Stokes' theorem for the helicoid Y(r, 0) = (r cos 0, r sin 0, 0) where (r, 0) lies in the rectangle [0, 1] × [0, π/2], and F is the vector field F = (7z, 8x, 4y). First, compute the surface integral: JMVXF). ds = f f f(r, 0)dr do, where a = b = = f(r, 0) = Finally, the value of the surface integral is g(0) = , C = Next compute the line integral on that part of the boundary from (1, 0, 0) to (0, 1, à/2). ſcF · dr = ſå g(0) d0, where a = ,b= d = (use "t" for theta). and (use "t" for theta). and
Transcribed Image Text:Verify Stokes' theorem for the helicoid Y(r, 0) = (r cos 0, r sin 0, 0) where (r, 0) lies in the rectangle [0, 1] × [0, π/2], and F is the vector field F = (7z, 8x, 4y). First, compute the surface integral: JMVXF). ds = f f f(r, 0)dr do, where a = b = = f(r, 0) = Finally, the value of the surface integral is g(0) = , C = Next compute the line integral on that part of the boundary from (1, 0, 0) to (0, 1, à/2). ſcF · dr = ſå g(0) d0, where a = ,b= d = (use "t" for theta). and (use "t" for theta). and
Expert Solution
Step 1

To find- Vertify Stokes' theorem for the helicoid ψr, θ = rcosθ, rsinθ, θ where r, θ lies in the rectangle 0, 1 × 0, π2, and F is the vector field F = 7z, 8x, 4y. 

First, compute the surface integral:

∬M∇×F·dS = ∫ab∫cdfr, θ dr dθ, where

a =        , b =       , c =        , d =       , and fr, θ =         

Finally, the value of the surface integral is        

Next compute the line integral on that part of the boundary from 1, 0, 0 to 0, 1, π2. 

∫CF·dr = ∫abgθ dθ, where

a =        , b =       , and gθ =        

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