MAT2500-01/03 21S Test 4 Print Name (Last, First) _________________________________|__Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use EQUAL SIGNS and arrows when appropriate. Always SIMPLIFY expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation IF appropriate). Indicate where technology is used and what type (Maple, GC). Only use technology to CHECK hand calculations, not substitute for them. Explain in as many words as possible everything you are doing!
Back all double integrals with a fully labeled diagram like bob always requests (consult previous tests, quizzes, handouts if in doubt).pledgeWhen you have completed the exam, please read and sign the dr bob integrity pledge and and scan this test sheet as a cover first page in the PDF scan of your lined paper hand work all on separate sheets."During this examination, all work has been my own. I give my word that I have not resorted to any ethically questionable means of improving my grade or anyone else's on this examination and that I have not discussed this exam with anyone other than my instructor, nor will I until after the exam period is terminated for all participants."Date: Signature:
1. Given 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 over the closed curve which is the counterclockwise oriented closed curve in the first quadrant which is the boundary of the region R between the three curves 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a) Make a diagram of this piecewise defined curve boundary and the region it encloses, finding the points of intersection and labeling them.b) Evaluate the line integral directly using a polar coordinate parametrization of the two circles [first express LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYrLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEnJiM5NTI7RicvRjBGNEYyRjxGMkY8RjJGPEYyRjw=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYvthen insert into 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] and use an obvious parametrization of the straight line segment. Be sure to state the simplified integrand before using technology to evaluate the iterated integral.c) Use Green's Theorem to evaluate the equivalent double integral, again in polar coordinates. Be sure to state the simplified integrand before using technology to evaluate the iterated integral.d) Check part c) using instead Cartesian coordinates to evaluate the double integral. You should get the same result.e) Optional. [Ignore this, it's for bob's amusement.] If you add the counterclockwise line integrals of the vector field 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 over the two circular curves in this boundary, you will get the area of the region, which you can check against either the Cartesian or polar double integral iteration for the area of this region R.
2. Given the parametrized curve 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 and the vector field 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.a) Set up and simplify the line integral of the vector field over this path, then use technology to evaluate it.b) Set up and simplify the line integral of this vector field on the straight line segment from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGMkZBRjJGQUYyRkE= to 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
c) Evaluate the divergence of this vector field.3. Consider the vector field 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 and the parametrized curve 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.a) Set up and simplify the line integral of the vector field over this path, then use technology to evaluate it.b) Show that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVElY3VybEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2Jy1GLDYjUSFGJy1GIzYmRjotSSZtb3ZlckdGJDYlLUYsNidRIkZGJy8lJWJvbGRHUSV0cnVlRicvRjBGRy9GM1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictSSNtb0dGJDYuUS0mUmlnaHRBcnJvdztGJy8lLHBsYWNlaG9sZGVyR0ZHRjIvJSZmZW5jZUdRJnVuc2V0RicvJSpzZXBhcmF0b3JHRlYvJSlzdHJldGNoeUdGRy8lKnN5bW1ldHJpY0dGVi8lKGxhcmdlb3BHRlYvJS5tb3ZhYmxlbGltaXRzR0ZWLyUnYWNjZW50R0ZWLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGX28vRlxvRkcvJStleGVjdXRhYmxlR0YxRjJGOkZjb0YyRjItRk82LVEiPUYnRjIvRlVGMS9GWEYxL0ZaRjEvRmZuRjEvRmhuRjEvRmpuRjEvRlxvRjEvRl5vUSwwLjI3Nzc3NzhlbUYnL0Zhb0ZgcC1JI21uR0YkNiRRIjBGJ0YyRmNvRjI= (hand derivatives in the formula) wherever this vector field is well defined and therefore admits a local potential function.
c) Solve the equations which determine that potential 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
d) Use it to evaluate the line integral between the endpoints of the above parametrized curve to check your work.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1. Green's TheoremThis closed loop has three piecewise contributions, first the line segment along the horizontal axis, then the right cemicirclular arc up to meet the other semicircular arc returning to the origin.We have done this so many times, the larger semicircle is 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 in polar coordinates. The smaller one is 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implicitplot approach gives the correct plot result without any problems in parametrization interfering.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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Here is the shading by equally spaced radial 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need the nonzero intersection point.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We insert these into 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we integrate in Cartesian coordinates, we have to separate the double integral into two separate integrals below and above the dividing black line, integrating along x first. To reverse the order of integration we would need 3 separate integrals.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Now the Green's Thm line 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 can look at the field plot in this region.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The intersection 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Solve the two arcs for x:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEnZXhwYW5kRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRjY2Ji1GIzYvLUklbXN1cEdGJDYlLUYsNiVRInhGJ0YvRjItRiM2JC1JI21uR0YkNiRRIjJGJy9GM1Enbm9ybWFsRidGSi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSIrRidGSi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGVS8lKXN0cmV0Y2h5R0ZVLyUqc3ltbWV0cmljR0ZVLyUobGFyZ2VvcEdGVS8lLm1vdmFibGVsaW1pdHNHRlUvJSdhY2NlbnRHRlUvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0Zeby1GPzYlLUY2NiQtRiM2Ji1GLDYlUSJ5RidGL0YyLUZQNi1RKCZtaW51cztGJ0ZKRlNGVkZYRlpGZm5GaG5Gam5GXG9GX28tRkc2JFEiMUYnRkpGSkZKRkRGTC1GUDYtUSI9RidGSkZTRlZGWEZaRmZuRmhuRmpuL0Zdb1EsMC4yNzc3Nzc4ZW1GJy9GYG9GZHBGXXAtRlA2LVEiLEYnRkpGUy9GV0YxRlhGWkZmbkZobkZqbi9GXW9RJjAuMGVtRicvRmBvUSwwLjMzMzMzMzNlbUYnLUY/NiUtRjY2JC1GIzYmRkFGam9GRkZKRkpGREZMRk8tRj82JUZnb0ZERkxGYHAtRkc2JFEiNEYnRkovJStleGVjdXRhYmxlR0ZVRkpGSi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZpcUZKRkotRlA2LVEiO0YnRkpGU0ZpcEZYRlpGZm5GaG5Gam5GanBGZXAtRiw2JVEkbWFwRidGL0YyLUY2NiQtRiM2KS1GLDYlUSZzb2x2ZUYnRi9GMkZmcC1GLDYlUSIlRidGL0YyRmZwRkFGaXFGSkZKRmlxRko=And the Green's Thm double integral in Cartesian 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 the Green's Thm double integral in polar 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 two different but equivalent trig expressions in the area.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1. Green's Theorem alternate problemThis closed loop has three piecewise contributions, first the line segment along the horizontal axis, then the right cemicirclular arc up to meet the other semicircular arc returning to the origin.We have done this so many times, the upper semicircle is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUkjbWlHRiQ2JlEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIjRGJ0YyRjwtRjk2LlEifkYnRjJGPEY+RkBGQkZERkZGSEZKL0ZNUSYwLjBlbUYnL0ZQRlktRiw2JlEkc2luRicvRjBGNEYyRjwtSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUScmIzk1MjtGJ0ZobkYyRjxGMkY8RjJGPC1GOTYuUSIsRidGMkY8Rj4vRkFGMUZCRkRGRkZIRkpGWC9GUFEsMC4zMzMzMzMzZW1GJ0Zeb0Y4LUZSNiVRIjBGJ0YyRjwtRjk2LlEjLi5GJ0YyRjxGPkZARkJGREZGRkhGSi9GTVEsMC4yMjIyMjIyZW1GJ0ZaLUkmbWZyYWNHRiQ2KC1GLDYmUSUmcGk7RidGaG5GMkY8LUYjNiYtRlI2JVEiMkYnRjJGPEYvRjJGNS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGX3EvJSliZXZlbGxlZEdGNEYyRjw= in polar coordinates. The lower one is 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need the nonzero intersection point.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We insert these into 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 using LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUScmIzk1MjtGJy9GMEY0RjJGPEYyRjw=: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For the area as a check, we integrate this over the two arcs.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Now the Green's Thm line 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmZXZhbGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSlHcmVlblJIU0YnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZARj1GQA==The implicitplot approach gives the correct result without any problems in parametrization interfering.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The intersection 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Solve the two arcs for x: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Here is the area in Cartesian coordinates.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And the Green's Thm double 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 two different trig expressions in the area.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEmQXJlYUdGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLUYsNiVRJkFyZWFDRidGL0YyRjUtRiw2JVEmQXJlYVBGJ0YvRjIvJStleGVjdXRhYmxlR0Y9Rjk=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This new angle 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 is the angle of a 3-4-5 triangle standing up (3 horizontal, 4 vertical). with 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so LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEnYXJjdGFuRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2JS1JJm1mcmFjR0YkNigtSSNtbkdGJDYlUSIxRidGMkY0LUYjNiYtRkA2JVEiMkYnRjJGNC9GMFEldHJ1ZUYnRjIvRjVRJ2l0YWxpY0YnLyUubGluZXRoaWNrbmVzc0dGQi8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZQLyUpYmV2ZWxsZWRHRjFGMkY0RjJGNC1JI21vR0YkNi5RIj1GJ0YyRjQvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Zjby1GVjYuUSJ+RidGMkY0RllGZW5GZ25GaW5GW29GXW9GX28vRmJvUSYwLjBlbUYnL0Zlb0Zqby1GPTYoLUYsNiZRJyYjOTY2O0YnRi9GMkY0RkNGTEZORlFGU0YyRjQ=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoZGlzcGxheUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzY0LUYsNiVRJXBsb3RGJ0YvRjItRjY2JC1GIzY+LUkjbW5HRiQ2JFEiMkYnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZNLyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmZuLUYsNiVRJGNvc0YnL0YwRk1GRS1GNjYkLUYjNiUtRiw2JVEidEYnRi9GMi8lK2V4ZWN1dGFibGVHRk1GRUZFLUZINi1RIixGJ0ZFRksvRk9GMUZQRlJGVEZWRlhGWi9GaG5RLDAuMzMzMzMzM2VtRidGYW8tRkg2LVEiPUYnRkVGS0ZORlBGUkZURlZGWC9GZW5RLDAuMjc3Nzc3OGVtRicvRmhuRmBwLUZCNiRRIjBGJ0ZFLUZINi1RIy4uRidGRUZLRk5GUEZSRlRGVkZYL0ZlblEsMC4yMjIyMjIyZW1GJ0Znbi1JJm1mcmFjR0YkNigtRiw2JVEnJiM5NjA7RidGXG9GRS1GIzYlRkFGL0YyLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZncS8lKWJldmVsbGVkR0ZNRmZvLUYsNiVRJ2Nvb3Jkc0YnRi9GMkZccC1GLDYlUSZwb2xhckYnRlxvRkVGZm8tRiw2JVEoc2NhbGluZ0YnRi9GMkZccC1GLDYlUSxjb25zdHJhaW5lZEYnRi9GMkZmby1GLDYlUSZjb2xvckYnRi9GMkZccC1GLDYlUSRyZWRGJ0YvRjJGZm8tRiw2JVEqdGhpY2tuZXNzRidGL0YyRlxwLUZCNiRRIjRGJ0ZFRmRvRkVGRUZmby1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0Zmbi8lJmRlcHRoR0Zpcy8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GZXM2JkZnc0Zqc0ZcdC9GX3RRJWF1dG9GJ0Y6LUY2NiQtRiM2PUZhc0ZHLUYsNiVRJHNpbkYnRlxvRkUtRjY2JC1GIzYkRmFvRkVGRUZmb0Zhb0ZccEZicEZlcC1GW3E2KC1GLDYlUSUmcGk7RidGXG9GRS1GIzYkRkFGRUZicUZlcUZocUZqcUZmb0ZcckZccEZfckZmb0ZickZccEZlckZmb0ZockZccC1GLDYlUSVibHVlRidGL0YyRmZvRl5zRlxwRmFzRkVGRUZmb0Zkc0ZhdEY6LUY2NiQtRiM2LS1GNjYmLUYjNictRjY2Ji1GIzYnRmJwRmZvRmJwRmRvRkVGRS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Zmby1GNjYmLUYjNidGQUZmb0ZicEZkb0ZFRkVGZnZGaXZGZG9GRUZFRmZ2Rml2RmZvRmhyRlxwLUYsNiVRJmdyZWVuRidGL0YyRmZvRl5zRlxwRmFzRmRvRkVGRUZmby1GLDYlUSpncmlkbGluZXNGJ0YvRjJGXHAtRiw2JUYxRi9GMkZkb0ZFRkVGZG9GRQ==2. 3d line integralboth curves start and end in the same points. They happen to belong to the same surface of revolution.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3. conservative vector fieldHere LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIjFGJ0YyRjxGMkY8 is set, but all results are proportional to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn for the test.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TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5OTk3MTg1MTE0MTA4WColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQiIiFGKUYpRiU=TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5OTk3MTg1MTE0NjUyWColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQiIiJGKUYpRiU=