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Question: area of polar curve

Question:area of polar curve

gilbert 5 Maple
area polar implicitplot plotting
December 15 2010
1

hoping someone can help me, one of my exam prep exercises asks the following

"

Consider the equation x^2+y^2 = 2+cos(x)*sin(y). Transform the equation into polar coordinates
using the ”subs” routine, and plot the resulting equation in polar coordinates (read the helppages
of plot to find the syntax for polar plots). Evaluate an appropriate integral to find the
area enclosed by the curve.  "

 

I did the conversion and plotting by

with(plots):
f:= x^2+y^2-2-cos(x)*sin(y);
subs([x^2+y^2=r^2], f);
subs([y=r*sin(theta), x=r*cos(theta)], %);
g:=simplify(%);
implicitplot(g,r=0..5,theta=0..2*Pi,coords=polar);

but I'm not sure how to get the area enclosed by the curve.

Thank you
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