1. AP problem back ch 7: skip # 7
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Agenda :
-Review
Hw p- 503 ;1-13 odd, odd,24
AP problem back ch 7: skip # 7
DESK
Warm-up (in your notes)
homework

2. LT3: Find the volume of a non-rotational solid with known cross sections

3. Area formula Distance S
LT3: Find the volume of a non-rotational solid with known cross sections
Area formula
Distance S

4. With perpendicular cross section to the x-axis squares
Find volume of solid with base bounded by
With perpendicular cross section to the x-axis squares

5. With perpendicular cross section to the x-axis squares
Find volume of solid with base bounded by
And
With perpendicular cross section to the x-axis squares

6. With perpendicular cross section to the y-axis squares
Find volume of solid with base bounded by
With perpendicular cross section to the y-axis squares
And

7. With perpendicular cross section to the x-axis rectangle with height 5
Find volume of solid with base bounded by
And
With perpendicular cross section to the x-axis rectangle with height 5

8. Find volume of solid with base bounded by
And
With perpendicular cross section to the x-axis isosceles right triangles . With a leg on the xy plane

9. Find volume of solid with base bounded by
With perpendicular cross section to the x-axis isosceles right triangles . With hypotenuse on xy plane
And

13. More Examples

15. Find the area of the region bounded by the two curves
LT1: Find the area between two curves.
Find the area of the region bounded by the two curves

16. LT1: Find the area between two curves.
Sketch the region bounded by the graphs of the equations and find the area of the region

17. Find the area of the region
LT1: Find the area between two curves.
Find the area of the region
You may use a calculator to evaluate the answer, but be sure to write the integral setup.

18. Given the area between ,x = 6, and y =0
LT1: Find the area between two curves.
Given the area between ,x = 6, and y =0
Find the line x = a such that the area is divided into two equal regions

19. ~20.106 LT2: Find the volume of a rotational solid.
Find the volume of the solid created when the region bounded by
is rotated around the y axis.
~20.106

20. LT2: Find the volume of a rotational solid.
Find the volume of the solid created when the region bounded by
is rotated around the x axis.

21. LT2: Find the volume of a rotational solid.
Find the volume of the solid created when the region bounded by
is rotated around the y = 2

22. LT2: Find the volume of a rotational solid.
Find the volume of the solid created when the region bounded by
is rotated around the x= 7

23. is rotated around the x = -1.
LT2: Find the volume of a rotational solid.
Find the volume of the solid created when the region bounded by
is rotated around the x = -1.
~36.861

24. LT2: Find the volume of a rotational solid.

25. LT3: Find the volume of a non-rotational solid with known cross sections

26. LT1: area between two curves
Write but do not solve an integral to find the line x = k. that divides the area R in equal halves. OR

27. LT3: Find the volume of a non-rotational solid with known cross sections

28. LT3: Find the volume of a non-rotational solid with known cross sections
Write but do not evaluate an integral to find the volume of the solid whose base is R if all cross sections perpendicular to the x axis are isosceles right triangles, with a leg as a base

29. Find the area bounded by the two equation from 0 and 1
LT3: Find the volume of a non-rotational solid with known cross sections
Find the area bounded by the two equation from 0 and 1

30. LT3: Find the volume of a non-rotational solid with known cross sections
Write but do not evaluate an integral to find the volume of the solid whose base is R if all cross sections perpendicular to the x axis are semicircles.

31. LT3: Find the volume of a non-rotational solid with known cross sections
Find the volume of the solid created with R as the base if the cross sections perpendicular to the y axis are squares.
You may use a calculator to evaluate the answer, but be sure to write the integral setup.

32. LT 2 Volume of rotational solid
About the y – axis

33. LT 2 Find the volume of the solid revolved about the given axis
LT 2 Find the volume of the solid revolved about the given axis. And bounded by the following equation: