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Disks, Washers, and Cross Sections Review. Let R be the region in the first quadrant under the graph of c)Setup but do not evaluate the integral necessary.

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Presentation on theme: "Disks, Washers, and Cross Sections Review. Let R be the region in the first quadrant under the graph of c)Setup but do not evaluate the integral necessary."— Presentation transcript:

1 Disks, Washers, and Cross Sections Review

2 Let R be the region in the first quadrant under the graph of c)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.

3 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.

4 Let functions f and g be defined by f(x) = x and, where k is a positive constant a)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. b)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.

5 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 R a)Setup but do not evaluate the integral representing the volume of the solid generated when R is revolved around the x-axis. b)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.

6 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.

7 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 a)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. b)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.

8 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) 2.80 b) 2.83 c) 2.86 d) 2.89 e) 2.92

9 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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