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Problem 3

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1. Find the area bounded by the curve , the x-axis, and the lines and .

2. Find the area of the ellipse .

3. Find the area bounded by the curve , for .

4. Find the area of the lemniscate .

5. Find the length of the cissoid from to .

6. Find the area bounded by the parabola and the straight line .

7. Find the area bounded by the ellipse .

8. Find the area of the ellipse whose parametric equations are and .

9. Find the parabola from (0,0) to (-4,4).

10. Find the area bounded by the parabola , the x-axis, and the lines and .

11. Find the bounded area between the curves and .

12. Find the area of an arch of the cycloid and where .

13. Find the area of the cardioid .

14. Find the area of one loop of the curve .

15. Find the area between the curve where and its asymptote.

16. Sketch the graph and find the area of the loop.

17. Sketch the graph and find the area between the curve and its asymptote.

18. Find the area in the first quadrant between the graph of , the coordinate axes, and the vertical line .

19. Find the circumference of a circle of radius R.

20. Find the entire length of the hypocycloid .

21. Find the volume of the solid generated by revolving about the x-axis the area bounded by the curve and the lines x=0 and y=8.

22. Find the volume of the solid generated by revolving about the line y=8 the area bounded by the curve and the lines x=0 and y=8.

23. The area bounded by the curve xy=1 and the lines x=1, x=3 and y=0 is evolved about the x-axis. Find the volume generated.

24. The smaller segment cut from the circle by the line y=1 is revolved about that line. Find the volume generated.

25. Find the volume generated by revolving about the line y=x the area bounded by the line and the parabola .

26. The area bounded by the hyperbola and the line x=6 is revolved about the y-axis. Find the volume generated.

27. Find the volume generated by revolving about the line x=2, the area bounded by the parabola and the line .

28. Find the area of the surface generated by revolving the curve about the initial line.

29. Find the area of the surface generated by revolving the curve about the line .

30. Find the area of the surface generated by revolving an arch of the cycloid , where about the x-axis.

 


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