Presentation is loading. Please wait.

Presentation is loading. Please wait.

Section 5.3 - Volumes by Slicing 7.3 Solids of Revolution I can use the definite integral to compute the volume of certain solids. Day 2: 1. 02111a-d Let.

Similar presentations


Presentation on theme: "Section 5.3 - Volumes by Slicing 7.3 Solids of Revolution I can use the definite integral to compute the volume of certain solids. Day 2: 1. 02111a-d Let."— Presentation transcript:

1 Section Volumes by Slicing 7.3 Solids of Revolution I can use the definite integral to compute the volume of certain solids. Day 2: a-d Let f be the function defined by a.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

2 rotating region

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

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

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

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

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

8 Let R be the first quadrant region enclosed by the graph of a) Find the area of R in terms of k. b)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? NO CALCULATOR

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 b)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 Let R be the region in the first quadrant under the graph of a) Find the area of R. b)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? c)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. CALCULATOR REQUIRED

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 b)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 c)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 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.

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 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.

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) 2.79 b) 2.82 c) 2.85 d) 2.88 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


Download ppt "Section 5.3 - Volumes by Slicing 7.3 Solids of Revolution I can use the definite integral to compute the volume of certain solids. Day 2: 1. 02111a-d Let."

Similar presentations


Ads by Google