Calculus AB AP
Practice Problem: Sec 7.1-7.3
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1. The area of the region bounded by the line , , and and the curve is
(a)
(b)
(c) *
(d)
(e)
2. What is the area of the region completely bounded by the curve and the line ?
(a)
(b)
(c) *
(d)
(e)
3. The area of the shaded region in the figure to the right is represented by which of the following integrals?
(a)
(b)
(c)
(d) *
(e)
4. The area of the region in the first quadrant enclosed by the graph of and the x-axis is
(a) *
(b)
(c)
(d)
(e) 1
5. Which of the following represents the area of the shaded region in the figure to the right?
(a)
(b) *
(c)
(d)
(e)
6. The area of the region enclosed by the graphs of and is
(a) *
(b)
(c)
(d)
(e) 1
7. The region in the first quadrant between the x-axis and the graph of is rotated around the y-axis. The volume of the resulting solid of revolution is given by
(a)
(b) *
(c)
(d)
(e)
8. The base of a solid is the region in the first quadrant enclosed by the parabola , the line , and the x-axis. Each plane section of the solid perpendicular to the x-axis is a square. The volume of the solid is
(a)
(b)
(c)
(d) *
(e)
9. Let R be the region between the graphs of and from to . The volume of the solid obtained by revolving R about the x-axis is given by
(a)
(b)
(c)
(d)
(e) *
10. Let R be the region in the first quadrant enclosed by the graph of , the line , the x-axis, and the y-axis. The volume of the solid generated when R is revolved about the y-axis is given by
(a)
(b) *
(c)
(d)
(e)
11. What is the volume of the solid generated by rotating about the x-axis the region enclosed by the curve and the lines , , and ?
(a)
(b)
(c) *
(d)
(e)
12. If the region enclosed by the y-axis, the line , and the curve is revolved about the y-axis, the volume of the solid generated is
(a) *
(b)
(c)
(d)
(e)
13. When the region enclosed by the graphs of and is revolved about the y-axis, the volume of the solid generated is given by
(a)
(b)
(c)
(d)
(e) *
14. The base of a solid is the region in the first quadrant enclosed by the graph of and the coordinate axes. If every cross section of the solid perpendicular to the y-axis is a square, the volume of the solid is given by
(a)
(b) *
(c)
(d)
(e)
15. Free Response: Let R be the region in the first quadrant enclosed by the graphs of and , as shown in the figure above.
(a) Find the area of R.
(b) The region R is the base of a solid. For this solid, at each x the cross section perpendicular to the x-axis has area . Find the volume of this solid.
(c) Another solid has the same base R. For this solid, the cross sections perpendicular to the y-axis are squares. Write, but do not evaluate, an integral expression for the volume of this solid.
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