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INTEGRAL CALCULUS
Problem 1. Find indefinite integrals
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Problem 2. Calculate definite integrals
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Problem 3.
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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22. Stoer, J., Bulirsch , R. (1993), Introduction to Numerical Analysis, 2nd ed., Springer-Verlag (New York).
23. Strang, G. (1988), Linear Algebra and Its Applications, 3rd ed., Harcourt, Brace, Jovanovich (San Diego).
24. Strang, G. (1991), Calculus, Wellesley-Cambridge Press (Wellesley, MA).
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27. Watson, G.N. (1944), A Treatise on the Theory of Bessel Functions, 2nd ed., Macmillan (New York).
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29. Wylie, C.R. (1995), Advanced Engineering Mathematics, 6th ed., McGraw-Hill (New York).
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Date: 2015-01-02; view: 1060
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