MAT2500-01/03 21S 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 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 when appropriate). Indicate where technology is used and what type (Maple, GC). Only use technology to CHECK hand calculations, not substitute for them.Find the volume under the surface 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 above the region of the plane between the 2 curves 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. First set up the three iterated integrals representing this volume and in each case let Maple evaluate the double integral:
a) in Cartesian coordinates integrating first in the vertical direction,
b) in Cartesian coordinates integrating first in the horizontal direction, c) in polar coordinates.In each case accompany your work with a new iteration diagram to justify your interation, a diagram shaded by equally spaced linear cross-sections and a typical one with bullet point endpoints labeled by the equation of the starting and stopping values of the integration variable for the inner integral and with an arrowhead midway indicating the variable's increasing direction.d) Use Maple to evaluate each such integral exactly. Do they agree as they should?e)numerically evaluated to 4 significant digits?f) Use the Student[MultiCalculus]) command MultiInt to see which one of these three multistep evaluations is the least frightening. State your opinion. State the partial evaluation of the radial integration only for the polar coordinate version as a single integral over the polar angle.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Notice that the line divides the circle into two parts but the second larger region cannot be integrated over using a single integral, but must be broken up into two subregions, so the smaller region is clearly intended.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You don't need this command to know that the polar coordinate version has to be simplest.