LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=MAT2500-01 13S Quiz 8 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 arrows and equal signs when appropriate. Always simplify expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation when appropriate). Indicate where technology is used and what type (Maple, GC).1. Consider the integral 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 . a) Evaluate this iterated integral exactly (no decimals) with technology.
b) Deconstruct this integral, identifying its bounding curves, and make a diagram "shading in" the region of integration, and showing a typical cross-section with its directional arrow indicating the inner integration, labeling its endpoints properly. [Label axes, tickmarks, intercepts, etc.].c) Now re-express the bounding curves as a single quadratic condition and covert it to polar coordinates, solving for the radial variable, and then make a similar new diagram indicating the corresponding situation for polar coordinate integration, showing the typical radial cross-section with properly labeled endpoints (arrow in direction of increasing values of the radial coordinate). State the range of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= values in terms of \316\270.d) What is the angular range for \316\270? Explain.e) Write down the new iterated double integral and evaluate it using technology. Do you get the correct result? If not, can you find your error in setup?solution1.a)LUkkaW50RzYiNiQtRiM2JComLCYqJEkieEdGJCIiIyIiIiokSSJ5R0YkRixGLUYtRi9GLC9GLzssJC1JJXNxcnRHRiQ2IywmRitGLEYqISIiRjdGMy9GKzsiIiFGLA==QysqJiwmKiRJInhHNiIiIiMiIiIqJEkieUdGJ0YoRilGKUYrRihGKS1JJGludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJzYkSSIlR0YnRitGKSwmLUklZXZhbEdGLzYkRjIvRistSSVzcXJ0R0YuNiMsJkYmRihGJSEiIkYpLUY1NiRGMi9GKywkRjhGPEY8RiktRi02JEYyRiZGKSwmLUY1NiRGMi9GJkYoRiktRjU2JEYyL0YmIiIhRjw=b)LUklcGxvdEc2IjYnNyQtSSVzcXJ0RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJkkieEdGJCIiIyokRi5GLyEiIiwkRidGMS9GLjsiIiFGLy9JJ2ZpbGxlZEdGJEkldHJ1ZUdGKi9JJmNvbG9yR0YkSSVwaW5rR0YkL0koc2NhbGluZ0dGJEksY29uc3RyYWluZWRHRiQ=The region is described by 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 (vertical cross-sections, from bottom to top) as 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(sweeping from left to right). The arc is part of a circle of radius 1 with center 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is equivalent to 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 or 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.
For the corner point 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 of the arc of the circle, the polar angle is:LywoKiRJInhHNiIiIiMiIiIqJEkieUdGJkYnRihGJSEiIyIiIQ==QyctSSVzdWJzRyUqcHJvdGVjdGVkRzYlLyokSSJ4RzYiIiIjLCYqJEkickdGKkYrIiIiKiRJInlHRipGKyEiIi9GKSomRi5GLy1JJGNvc0c2JEYlSShfc3lzbGliR0YqNiNJJnRoZXRhR0YqRi9JIiVHRipGLy1JJnNvbHZlR0Y3NiRGO0YuRi8+SSNlcUdGKi9GLiZGOzYjRis=QyQtSSV3aXRoRzYiNiNJJnBsb3RzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlISIiLUkoZGlzcGxheUc2IjYlLUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYoLCQtSSRjb3NHRig2I0kmdGhldGFHRiQiIiMvRjA7LCRJI1BpR0YpISIiRjUvSSdjb29yZHNHRiRJJnBvbGFyR0YkL0koc2NhbGluZ0dGJEksY29uc3RyYWluZWRHRiQvSSdmaWxsZWRHRiRJJXRydWVHRikvSSZjb2xvckdGJEklcGlua0dGJC1GJzYnRixGMkY3RjovRkFJJmJsYWNrR0YkLUYnNiM3JDckIiIhRks3JC1JIipHRik2JCwkLUYuNiMsJEY1IyIiIiIiJ0YxRlEsJComRlFGVS1JJHNpbkdGKEZSRlVGMQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Thus:LUkkaW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtRiM2JC1JIipHRiU2JComSSJyR0YnIiIjLUkiXkdGJTYkKiZGLyIiIi1JJHNpbkdGJDYjSSZ0aGV0YUdGJ0Y1RjBGNUYvL0YvOyIiISwkLUkkY29zR0YkRjhGMC9GOTssJEkjUGlHRiUjISIiRjAsJEZDI0Y1RjA=Step-by-step, using the fact that for the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-substitution LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSRjb3NGJy9GMEY9RjktSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUScmIzk1MjtGJ0ZSRjlGOUY5Rjk=, then 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 to replace the sine by the factor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIxRidGL0Yv for the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= integrand (coefficient of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn):QysqJkkickc2IiIiJi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSZ0aGV0YUdGJSIiIyIiIi1JJGludEdGKTYkSSIlR0YlRiRGLywmLUklZXZhbEdGKjYkRjMvRiQsJC1JJGNvc0dGKUYsRi5GLy1GNjYkRjMvRiQiIiEhIiJGLy1GMTYkRjNGLUYvLCYtRjY2JEYzL0YtLCRJI1BpR0YqI0YvRi5GLy1GNjYkRjMvRi0sJEZII0ZARi5GQA==The theta integral needs technology to evaluate since we no longer teach products of powers of trig cofunction integrals.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=