illustrating double integrals in polar 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 region of the plane in the first quadrant is bounded by the three curves: 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
Verify Green's theorem using polar coordinates to describe the two semicircles and to evaluate the double integral.polar coordinate line integral problem and Green's TheoremGiven the line integral 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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.solutionThis 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 derive the following diagram below.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 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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 However, we rederive these first.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The implicitplot approach gives the correct plot result without any problems in parametrization interfering.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Next we make a nicer diagram.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Here is the shading by equally spaced radial cross-sections. First we set up some radial lines and arrows.First the arrow along the typical radial cross section and the final theta value radial line.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Next the equally spaced radial linear cross-sections, and the typical one "in the middle somewhere" that will have its bullet point endpoints labeled by the starting and stopping value equations for the radial variable.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 need the nonzero intersection point for the polar coordinate limits and the Cartesian double integral approach as a check.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We insert these into 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 using LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUScmIzk1MjtGJy9GMEY0RjJGPEYyRjw=:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVEjUDFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRKXNpbXBsaWZ5RidGL0YyLUZQNiQtRiM2Ji1GLDYlUSVzdWJzRidGL0YyLUZQNiQtRiM2Jy1GUDYmLUYjNiotRiM2Ki1GLDYlUSJyRidGL0YyLUY2Ni1RKSZlcXVhbHM7RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1JJm1mcmFjR0YkNigtRiM2Ki1JI21uR0YkNiRRIjRGJ0Y5LUY2Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GZXAtSSZtc3FydEdGJDYjLUZecDYkUSI1RidGOS8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GJy8lK2V4ZWN1dGFibGVHRj0vJSlyZWFkb25seUdGMS8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYnRjlGanAvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRlxyLyUpYmV2ZWxsZWRHRj1GXXFGYHFGYnFGZHFGOS1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIRmRwL0ZOUSwwLjMzMzMzMzNlbUYnLUYjNiotRiw2JVEoJnRoZXRhO0YnL0YwRj1GOUZlby1GIzYqLUYsNiVRJ2FyY3RhbkYnRlxzRjktRjY2LVEwJkFwcGx5RnVuY3Rpb247RidGOUY7Rj5GQEZCRkRGRkZIRmRwRmZwLUZQNiQtRiM2KC1GXnA2JFEiMkYnRjlGXXFGYHFGYnFGZHFGOUY5Rl1xRmBxRmJxRmRxRjlGXXFGYHFGYnFGZHFGOUZdcUZgcUZicUZkcUY5RjkvJSVvcGVuR1EnJmxjdWI7RicvJSZjbG9zZUdRJyZyY3ViO0YnRmFyLUZQNiYtRiM2LUZiby1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRmRwRmZwLUYsNiVRJGNvc0YnRlxzRjktRlA2JS1GIzYlLUYsNiZGW3NGXHNGYHFGOS9GZXFRKDJEfk1hdGhGJ0Y5RmBxRjlGYXJGYm9GZnQtRiw2JVEkc2luRidGXHNGOUZcdUZgcUY5RjkvRl10USJbRicvRmB0USJdRidGYHFGOUY5RmBxRjlGOUZgcUY5RjktRjY2LVEiO0YnRjlGO0ZkckZARkJGREZGRkhGZHBGTS1GLDYlUSNQMkYnRi9GMkY1LUZQNiYtRiM2K0ZdcC1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORml2RistRlA2Ji1GIzYlLUZecDYkRmlxRjlGYHFGOUY5Rmd1Rml1RmFyRistRlA2Ji1GIzYlRmlzRmBxRjlGOUZndUZpdUZgcUY5RjlGZ3VGaXVGYHFGOQ==Integrating x first then y only requires two separate double integrals (added together!). The bold horizontal dividing line separates the two subregions.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If 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.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY4LUkjbWlHRiQ2JVEjUjFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJ0RidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSomY29sb25lcTtGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVi1GNjYmLUYjNjMtSSNtbkdGJDYkUSI0RidGQC1GQzYtUSJ+RidGQEZGRkhGSkZMRk5GUEZSL0ZVUSYwLjBlbUYnL0ZYRl9vLUYsNiVRJGNvc0YnL0YwRj9GQEY1RltvRmFvRjUtRkM2LVEiLEYnRkBGRi9GSUYxRkpGTEZORlBGUkZeby9GWFEsMC4zMzMzMzMzZW1GJ0ZnbkZbb0Zhb0Y1RltvLUYsNiVRJHNpbkYnRmRvRkBGNUY9RkBGQC8lJW9wZW5HUScmbGFuZztGJy8lJmNsb3NlR1EnJnJhbmc7RictRkM2LVEiO0YnRkBGRkZob0ZKRkxGTkZQRlJGXm9GV0YrLUZDNi1RIidGJ0ZARkZGSEZKRkxGTkZQRlIvRlVRLDAuMTExMTExMWVtRidGYG9GNUZkcC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0Zfby8lJmRlcHRoR0ZhcS8lKmxpbmVicmVha0dRKG5ld2xpbmVGJ0Zbby1GLDYlUSNSMkYnRi9GMi1GNjYkLUYjNiRGOkZARkBGQi1GNjYmLUYjNjItRmhuNiRRIjJGJ0ZARltvRltwRlxyRltvRmFvRlxyRmVvRmRyRltvRltwRlxyRltvRltwRlxyRkBGQEZecEZhcEZkcEZpcUZncEZcckZkcEY9RkA=Now the Green's Thm line integral 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 :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 can look at the field plot in this region.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The intersection pointLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEmc29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Jy1GNjYmLUYjNi8tSSVtc3VwR0YkNiUtRiw2JVEieEYnRi9GMi1GIzYkLUkjbW5HRiQ2JFEiMkYnL0YzUSdub3JtYWxGJ0ZKLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIitGJ0ZKLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZVLyUpc3RyZXRjaHlHRlUvJSpzeW1tZXRyaWNHRlUvJShsYXJnZW9wR0ZVLyUubW92YWJsZWxpbWl0c0dGVS8lJ2FjY2VudEdGVS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRl5vLUY/NiUtRjY2JC1GIzYmLUYsNiVRInlGJ0YvRjItRlA2LVEoJm1pbnVzO0YnRkpGU0ZWRlhGWkZmbkZobkZqbkZcb0Zfby1GRzYkUSIxRidGSkZKRkpGREZMLUZQNi1RIj1GJ0ZKRlNGVkZYRlpGZm5GaG5Gam4vRl1vUSwwLjI3Nzc3NzhlbUYnL0Zgb0ZkcEZdcC1GUDYtUSIsRidGSkZTL0ZXRjFGWEZaRmZuRmhuRmpuL0Zdb1EmMC4wZW1GJy9GYG9RLDAuMzMzMzMzM2VtRictRj82JS1GNjYkLUYjNiZGQUZqb0ZGRkpGSkZERkxGTy1GPzYlRmdvRkRGTEZgcC1GRzYkUSI0RidGSi8lK2V4ZWN1dGFibGVHRlVGSkZKLyUlb3BlbkdRInxmckYnLyUmY2xvc2VHUSJ8aHJGJ0ZmcC1GNjYmLUYjNidGQUZmcEZnb0ZpcUZKRkpGW3JGXnJGaXFGSkZKLUYsNiNRIUYnRmlxRko=Solve the two arcs for x: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And the Green's Thm double integral in Cartesian coordinatesLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY8LUkjbWlHRiQ2JVEqR3JlZW5SSFNDRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSShtc3Vic3VwR0YkNictRjY2LVErJkludGVncmFsO0YnRjlGO0Y+L0ZBRjFGQi9GRUYxRkZGSC9GS1EmMC4wZW1GJy9GTkZYLUYjNiQtSSNtbkdGJDYkUSIwRidGOUY5LUYjNiQtSSZtZnJhY0dGJDYoLUYjNiQtRmduNiRRIjhGJ0Y5RjktRiM2JC1GZ242JFEiNUYnRjlGOS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXnAvJSliZXZlbGxlZEdGPUY5LyUxc3VwZXJzY3JpcHRzaGlmdEdGaW4vJS9zdWJzY3JpcHRzaGlmdEdGaW4tRlA2Jy1GNjYtRlRGOS9GPFEmdW5zZXRGJy9GP0ZccUZVL0ZDRlxxRlYvRkdGXHEvRklGXHFGV0ZZLUYjNiUtSSZtc3FydEdGJDYjLUYjNiktRjY2LVEqJnVtaW51czA7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORlxyLUklbXN1cEdGJDYlLUYsNiVRInlGJ0YvRjItRmduNiRRIjJGJ0Y5RmNwLUY2Ni1RJyZwbHVzO0YnRjlGO0Y+RkBGQkZERkZGSEZbckZdckZkci1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIRldGWUZhckY5LUYsNiNRIUYnRjktRiM2JkZkckZnci1GZHE2Iy1GIzYnRmhxRl5yRmdyLUZnbjYkUSI0RidGOUY5RjlGY3BGZXBGYXItRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSEZXRlktRjY2LVEwJkRpZmZlcmVudGlhbEQ7RidGOUZbcUZdcS9GQUZccUZecS9GRUZccUZfcUZgcUZXRlktRiw2JVEieEYnRi9GMkZpc0ZcdEZhci1GNjYtUSIrRidGOUY7Rj5GQEZCRkRGRkZIRltyRl1yLUZQNidGUi1GIzYkLUZdbzYoRmFvRmRvRmlvRlxwRl9wRmFwRjktRiM2JEZkckY5RmNwRmVwLUZQNidGaXAtRiM2JkZkckZocUZic0Y5LUYjNiZGXXNGYHNGXXNGOUZjcEZlcEZhckZpc0ZcdEZhdEZpc0ZcdEZhci1GNjYtUSI7RidGOUY7L0Y/RjFGQEZCRkRGRkZIRldGTS1GLDYlUSZldmFsZkYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRIiVGJ0YvRjJGOUY5LyUrZXhlY3V0YWJsZUdGPUY5And 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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Next for fun we evaluate the area enclosed by the three curves using Green's theorem applied to the vector field 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 whose divergence is 1.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Instead with Cartesian coordinates: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 polar coordinates.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 different trig expressions, but equivalent.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 complementary angle to arctan(2) when doubled gives the upright 3-4-5 triangle angle 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