1. Section 5.3 - Volumes by Slicing
I can use the definite integral to compute the volume of certain solids.
Day 2:
a-dLet f be the function defined by
Write an equation of the line normal to the graph of f at x = 1.
b. For what values of x is the derivative of f, f ‘ (x), not continuous? Justify your answer.
c. Determine the limit of the derivative at each point of discontinuity found in part (b).
d. Can be completed using the method of u-substitution? If yes, complete the integration. If no, explain why u-substitution
cannot be used for
Solids of Revolution
7.3

2. rotating region
rotating region
rotating region

3. Find the volume of the solid generated by revolving the regions
bounded by
about the x-axis.

4. Find the volume of the solid generated by revolving the regions
bounded by
about the x-axis.

5. Find the volume of the solid generated by revolving the regions
bounded by
about the y-axis.

6. Find the volume of the solid generated by revolving the regions
bounded by
about the x-axis.

7. Find the volume of the solid generated by revolving the regions
bounded by
about the line y = -1.

8. NO CALCULATOR
Let R be the first quadrant region enclosed by the graph of
a) Find the area of R in terms of k.
Find the volume of the solid generated when R is
rotated about the x-axis in terms of k.
c) What is the volume in part (b) as k approaches infinity?

9. Let R be the first quadrant region enclosed by the graph of
a) Find the area of R in terms of k.

10. Let R be the first quadrant region enclosed by the graph of
Find the volume of the solid generated when R is
rotated about the x-axis in terms of k.

11. Let R be the first quadrant region enclosed by the graph of
c) What is the volume in part (b) as k approaches infinity?

12. CALCULATOR REQUIRED
Let R be the region in the first quadrant under the graph of
a) Find the area of R.
The line x = k divides the region R into two regions. If the
part of region R to the left of the line is 5/12 of the area of
the whole region R, what is the value of k?
Find 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.

13. Let R be the region in the first quadrant under the graph of
a) Find the area of R.

14. Let R be the region in the first quadrant under the graph of
The line x = k divides the region R into two regions. If the
part of region R to the left of the line is 5/12 of the area of
the whole region R, what is the value of k? A

15. Let R be the region in the first quadrant under the graph of
Find 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.
Cross Sections

16. 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. Find the volume of the
solid in terms of a.

17. CALCULATOR REQUIRED

18. 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.

19. 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.

20. 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 closest to
a) b) c) d) e) 2.91

21. 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

22. CALCULATOR REQUIRED

23. NO CALCULATOR

24. CALCULATOR REQUIRED

25. NO CALCULATOR

26. CALCULATOR REQUIRED

27. CALCULATOR REQUIRED