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3. Practice using Stokes' theorem by evaluating the following line integrals. We can use Stokes' theorem because these are work integrals around loops in R. fa Let C be the piecewise curve from (0.0.0) to 2.0.) along 2, then in a straight line to (2, 1,1), then down to (0,1,0) along z = r2, and then in a straight tise back to (0,0.0) # Fr u. z) = (e +2?,7-,+ 2") then calculate o F- (b) Let C = C1+C2 where C1 is parametrized by (cos t,0, sin t) for 0

3. Practice using Stokes' theorem by evaluating the following line integrals. We can use Stokes' theorem because these are work integrals around loops in R. fa Let C be the piecewise curve from (0.0.0) to 2.0.) along 2, then in a straight line to (2, 1,1), then down to (0,1,0) along z = r2, and then in a straight tise back to (0,0.0) # Fr u. z) = (e +2?,7-,+ 2") then calculate o F- (b) Let C = C1+C2 where C1 is parametrized by (cos t,0, sin t) for 0

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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3. Practice using Stokes' theorem by evaluating the following line integrals. We can use Stokes' theorem because these are work integrals around loops in R³. fa Let C be the piecewise curve from (0.0.0) to (2.0. 4) along (2, 1,4), then down to (0,1,0) along z = x?, and then in a straight lise back to (0,0,0) H E( u. 2) = (e" + 2², r - y², 2² + 2°) then calculate r 2, then in a straight line to %3D Fdr. (b) Let C = C1+C2 where C1 is parametrized by (cos t, 0, sin t) for 0 <t<n and C2 is parametrized by (- cos t, sin t, 0) for 0 <t < T. Calculate the work done by the vector field (2x – 3y, r + 4y, 5y – 2). (c) Let C be the curve of intersection between the cylinder r2 + =1 and the hyperbolic paraboloid 2²-y? = 2, oriented clockwise when viewed from above. If G(r, y, 2) = (3x2y – 2, a + 5,322 – 2rz) then calculate G. dr.
Transcribed Image Text:3. Practice using Stokes' theorem by evaluating the following line integrals. We can use Stokes' theorem because these are work integrals around loops in R³. fa Let C be the piecewise curve from (0.0.0) to (2.0. 4) along (2, 1,4), then down to (0,1,0) along z = x?, and then in a straight lise back to (0,0,0) H E( u. 2) = (e" + 2², r - y², 2² + 2°) then calculate r 2, then in a straight line to %3D Fdr. (b) Let C = C1+C2 where C1 is parametrized by (cos t, 0, sin t) for 0 <t<n and C2 is parametrized by (- cos t, sin t, 0) for 0 <t < T. Calculate the work done by the vector field (2x – 3y, r + 4y, 5y – 2). (c) Let C be the curve of intersection between the cylinder r2 + =1 and the hyperbolic paraboloid 2²-y? = 2, oriented clockwise when viewed from above. If G(r, y, 2) = (3x2y – 2, a + 5,322 – 2rz) then calculate G. dr.
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