Exam 10: Section 5: Conics, Parametric Equations, and Polar Coordinates

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Find the length of the curve over the given interval. Find the length of the curve over the given interval.

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Find the length of the curve over the given interval. Find the length of the curve over the given interval.

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Find the area of the interior of Find the area of the interior of   . .

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Find the area of the surface formed by revolving about the Find the area of the surface formed by revolving about the   axis the following curve over the given interval.  axis the following curve over the given interval. Find the area of the surface formed by revolving about the   axis the following curve over the given interval.

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Find the points of intersection of the graphs of the equations Find the points of intersection of the graphs of the equations   . .

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Find the area of the region lying between the loops of Find the area of the region lying between the loops of   . .

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Find the length of the curve Find the length of the curve   over the interval   . over the interval Find the length of the curve   over the interval   . .

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Find the area of the common interior of the polar equations Find the area of the common interior of the polar equations   by sketching the graph of the equations using the graphing utility. by sketching the graph of the equations using the graphing utility.

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Find the area of inside Find the area of inside   and outside   by sketching the graph of the equations using the graphing utility. and outside Find the area of inside   and outside   by sketching the graph of the equations using the graphing utility. by sketching the graph of the equations using the graphing utility.

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Find the length of the curve over the given interval. Find the length of the curve over the given interval.

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Write an integral that represents the area of the shaded region for Write an integral that represents the area of the shaded region for   as shown in the figure. Do not evaluate the integral.  as shown in the figure. Do not evaluate the integral. Write an integral that represents the area of the shaded region for   as shown in the figure. Do not evaluate the integral.

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Find the area of one petal of Find the area of one petal of   . .

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Find the area of the surface formed by revolving about the polar axis the following curve over the given interval. Find the area of the surface formed by revolving about the polar axis the following curve over the given interval.

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Find all points of intersection of the graphs of the equations. Find all points of intersection of the graphs of the equations.

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Find the points of intersection of the graphs of the equations. Find the points of intersection of the graphs of the equations.

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Find the area of the inner loop of Find the area of the inner loop of   . .

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Find the area of the interior of Find the area of the interior of   . .

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Find the length of the curve Find the length of the curve   over the interval   . Round your answer to two decimal places. over the interval Find the length of the curve   over the interval   . Round your answer to two decimal places. . Round your answer to two decimal places.

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