parametrizing the points in a region using Cartesian coordinates
justifying the iteration of a double integralexecute worksheet (!!!) before using 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 : LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkobXN1YnN1cEdGJDYnLUkjbW9HRiQ2LlErJkludGVncmFsO0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZ1bnNldEYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHUSV0cnVlRicvJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkotRiM2JS1JJm1mcmFjR0YkNigtSSNtbkdGJDYlUSIxRidGMkY1LUYjNiYtRlM2JVEiMkYnRjJGNS8lJ2l0YWxpY0dGP0YyL0Y2USdpdGFsaWNGJy8lLmxpbmV0aGlja25lc3NHRlUvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXW8vJSliZXZlbGxlZEdGNEYyRjUtRiM2JS1GUDYoLUZTNiVRIjNGJ0YyRjVGVkZpbkZbb0Zeb0Zgb0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUvc3Vic2NyaXB0c2hpZnRHRltwLUYsNidGLi1GIzYnRlItRi82LlEiK0YnRjJGNS9GOUY0L0Y8RjQvRj5GNC9GQUY0L0ZDRjQvRkVGNC9GR0Y0L0ZJUSwwLjIyMjIyMjJlbUYnL0ZMRl1xLUZQNigtRiM2Ji1JJW1zdXBHRiQ2JS1JI21pR0YkNiZRInhGJ0ZlbkYyRmduRlZGaW9GZW5GMkZnbkZWRmluRltvRl5vRmBvRjJGNS1GIzYnLUZTNiVRIjVGJ0YyRjUtRi82LlEoJm1pbnVzO0YnRjJGNUZlcEZmcEZncEZocEZpcEZqcEZbcUZccUZecS1GUDYoRmNxRlZGaW5GW29GXm9GYG9GMkY1RmlvRlxwLUZncTYmUSJmRidGZW5GMkZnbi1JKG1mZW5jZWRHRiQ2JS1GIzYnRmZxLUYvNi5RIixGJ0YyRjVGZXAvRjxGP0ZncEZocEZpcEZqcEZbcUZIL0ZMUSwwLjMzMzMzMzNlbUYnLUZncTYmUSJ5RidGZW5GMkZnbkYyRjVGMkY1LUYvNi5RIn5GJ0YyRjVGZXBGZnBGZ3BGaHBGaXBGanBGW3FGSEZLLUYvNi5RMCZEaWZmZXJlbnRpYWxEO0YnRjJGNUY4RjsvRj5GOkZAL0ZDRjpGREZGRkhGS0Zic0Zlc0Zoc0ZmcUYyRjU=Skip down to the explanation under the slider plot. This attempts to make concrete the idea of representing an iterated double integral in polar coordinates by a diagram of the region of integration with a typical radial cross-section line segment with bullet point endpoints (labeled by the equations of the inner and outer bounding curves 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 giving the starting and stopping values of the radial coordinate for each value of the polar angle, and then labeling the starting and stopping line segments LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI9RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSy1GLDYmUScmIzk0NTtGJ0YvRjJGNC1GODYuUSIsRidGMkY0RjsvRj5RJXRydWVGJ0Y/RkFGQ0ZFRkcvRkpRJjAuMGVtRicvRk1RLDAuMzMzMzMzM2VtRidGK0Y3LUYsNiZRJyYjOTQ2O0YnRi9GMkY0RjJGNA== which provide the other bounding curves of the region of integration. The arrow head indicates the direction of increasing radial variable in the inner integral.For this Explore plot, I cannot make moving labels, so I will leave them off, but these are essential in your hand diagrams necessary to justify any iterated double integral you write down on a quiz or test in dr bob's classes.plot 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
To make the simple Explore work, we use the fraction of the vertical cross-section LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn instead of the actual coordinate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn so that we have a fixed interval for its slider as required.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n corresponds to: 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 each value pf x we trace out the points along the vertical cross-section of the region of integration, then we sweep the whole vertical cross-section line segment over the region of integration. This corresponds to first doing the inner integral of the iterated double integral, then the outer integral. We sweep up all the values of the function over the region of integration in a systematic way.As we increase LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn from left to right on its slider, we move upward along the vertical cross-section, sweeping up the points along the way (symbolized by the thickening of the line as we move along it.
As we slide x from left to right on its slider, we move the entire vertical cross-section from left to right, sweeping up all the points in the region of integration.threeway iteration example: Cartesian in both orders, 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diagram shows the three possible ways of iterating an integral over this region of the plane, two in Cartesian coordinates, one in polar coordinates. Typical linear cross-sections representing the inner integral are shown. The region is enclosed by the two curves: 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
The three parametrizations of the region:y-first: 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
x-first: 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
r-first: 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