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13 Nov 2019
3. Use Stokes' theorem to evaluate the line integral dr where F(x, y, z) = (x2-v)i + 4: +12k and the closed curve C is obtained by cutting the cone r2 yī by the plane 2, oriented counterclockwise as viewed from above.
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Bunny Greenfelder
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Help Entering Answers (1 point) Use Stokes' Theorem to evaluate F dr where F(x, y, z) 5yzi 2xzj2ek and C is the ciry4,z 3 oriented counterclockwise as viewed from above. Since the circle is oriented counterclockwise as viewed from above the surface we attach to the circle is oriented upwards curl F = The easiest surface to attach to this curve is the disk x2 + y2 ã 4, z-3. Using this surface in Stokes' Theorem evaluate the following. F dr- J C where yi X2ã¼ Evaluate P-dr
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Help Entering Answers (1 point) Use Stokes' Theorem to evaluate F dr where F(x, y, z) 5yzi 2xzj2ek and C is the ciry4,z 3 oriented counterclockwise as viewed from above. Since the circle is oriented counterclockwise as viewed from above the surface we attach to the circle is oriented upwards curl F = The easiest surface to attach to this curve is the disk x2 + y2 ã 4, z-3. Using this surface in Stokes' Theorem evaluate the following. F dr- J C where yi X2ã¼ Evaluate P-dr
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Use Stokes' Theorem to evaluate F dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = 6y1+ xzj + (x + y)k, C is the curve of intersection of the plane z = y + 6 and the cylinder x2 + y2- 1.
HOMEWORK FOR MTH201- SUBMISSION DEADLINE: 30 NOVEMBER 2017 1. Use Greens' theorem to evaluate the line integral F.dr where F(zw) = (r-r'), (r' + rl, and C is the triangle bounded by y = 0, x = 3. and y = z, oriented clockwise. 2. Consider the line integral sin()co(r)dr+cos() siner)dy+d where C is the line segment from A(1,0,0) to B(0, 1,1) First show that the integral is independent from path and then calculate the integral by finding a potential function 3. Use Stokes' theorem to evaluate the line integral F.dr where Fir, y, a) +4j+k, and the closed curve C is obtained by cutting the cone ;-VET+ by the plane :-2, oriented counterclockwise as viewed from above 4. Use the divergence theore to find the flux of the vector field (r,y,) fi + rj + 'k outward through the surface of the sphere r2 +2 = a2 (a > 0). Date: Novenbser 20, 2017
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