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**Disks, Washers, and Cross Sections Review**

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**Let R be the region in the first quadrant under the graph of**

Setup but do not evaluate the integral necessary to compute the volume of the solid whose base is the region R and whose cross sections cut by planes perpendicular to the x-axis are squares.

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**The base of a solid is the circle . Each section of the**

solid cut by a plane perpendicular to the x-axis is a square with one edge in the base of the solid. Setup but doe not evaluate the integral to find the volume of the solid in terms of a.

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**Let functions f and g be defined by f(x) = x and , where**

k is a positive constant If R is the region between the graphs of f and g on the interval [1, 3], setup but do not evaluate an integral expression in terms of k for the volume of the solid generated when R is rotated about the x-axis. Setup up but do not evaluate an integral expression in terms of k for the volume of the solid generated when R is rotated about the horizontal line y = -2.

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**Let R be the region marked in the first quadrant enclosed by**

the y-axis and the graphs of as shown in the figure below Setup but do not evaluate the integral representing the volume of the solid generated when R is revolved around the x-axis. R Setup, but do not evaluate the integral representing the volume of the solid whose base is R and whose cross sections perpendicular to the x-axis are squares.

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**Setup, but do not evaluate, the integral necessary to find the**

volume of the solid formed when the region bounded by is revolved about the x-axis.

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**Let R be the region in the first quadrant bounded above by the**

graph of f(x) = 3 cos x and below by the graph of Setup, but do not evaluate, an integral expression in terms of a single variable for the volume of the solid generated when R is revolved about the x-axis. Let the base of a solid be the region R. If all cross sections perpendicular to the x-axis are equilateral triangles, setup, but do not evaluate, an integral expression of a single variable for the volume of the solid.

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**The volume of the solid generated by revolving the first quadrant**

region bounded by the curve and the lines x = ln 3 and y = 1 about the x-axis is a) b) c) d) e) 2.92

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**The base of a solid is a right triangle whose perpendicular sides**

have lengths 6 and 4. Each plane section of the solid perpendicular to the side of length 6 is a semicircle whose diameter lies in the plane of the triangle. The volume of the solid in cubic units is: a) 2pi b) 4pi c) 8pi d) 16pi e) 24pi

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Warm Up Show all definite integrals!!!!! 1)Calculator Active: Let R be the region bounded by the graph of y = ln x and the line y = x – 2. Find the area.

Warm Up Show all definite integrals!!!!! 1)Calculator Active: Let R be the region bounded by the graph of y = ln x and the line y = x – 2. Find the area.

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