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* Calculus : Area in polar coordinate.

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Windows : Dev-C++ 4
Linux : gcc abc.c -lm Return
a.out Return

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* You can compile the *.c files directly without create a project.

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If f is continuous and f(k) >= 0 on [a,b],

where 0 <= a < b <= 2Pi,

then the area A of the region bounded by the
graphs of r = f(k) with k = a and k = b is

/ b / b
| |
A = | 1/2 f(k)^2 dk = | 1/2 r^2 dk
| |
/ a / a

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c13d_1a.c fa.h : r= 2+2cos(k)
c13d_1b.c fb.h : r= 2cos(k)
c13d_1c.c fd.h : r= exp(k)

c13d_2d.c fd.h : r= 2+2sin(k)
c13d_2e.c fe.h : r= sin(2k)


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The area A of the region bounded by the graph of
two polar equations r = f(k) and r = g(k) and
the line k = a and k = b is

/ b / b
| |
A = | 1/2 f(k)^2 dk - | 1/2 g(k)^2 dk
| |
/ a / a

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c13d_3g.c fg.h : r=2+2cos(k); r=3;
c13d_3h.c fh.h : r=4*cos(2k); r=2;


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The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c13d.zip