document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=404203>Question 404203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the area bounded by the curve r=2acos(&#952;) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #285676 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=285676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For polar coordinates, the area would be given by the integral\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29int%28r%5E2%2C+d%28theta%29%2C+0%2C+pi%29%0D%0A=%281%2F2%29int%284a%5E2cos%5E2%28theta%29%2C+d%28theta%29%2C+0%2C+pi%29%0D%0A%0D%0A=+2a%5E2int%28cos%5E2%28theta%29%2C+d%28theta%29%2C+0%2C+pi%29%0D%0A%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2int%28%28cos%282theta%29+%2B+1%29%2C+d%28theta%29%2C+0%2C+pi%29 ALIGN=MIDDLE  ALT=\"a%5E2int%28%28cos%282theta%29+%2B+1%29%2C+d%28theta%29%2C+0%2C+pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%28sin%282theta%29%2F2+%2B+theta%29%5B0%5D%5E%28pi%29%29 ALIGN=MIDDLE  ALT=\"a%5E2%28sin%282theta%29%2F2+%2B+theta%29%5B0%5D%5E%28pi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%28sin%282pi%29%2F2+%2B+pi+-+sin0%2F2+-+0%29 ALIGN=MIDDLE  ALT=\"a%5E2%28sin%282pi%29%2F2+%2B+pi+-+sin0%2F2+-+0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2pi ALIGN=MIDDLE  ALT=\"a%5E2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "NOTE: The polar equation is equivalent to the circle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+a%29%5E2+%2B+y%5E2+=+a%5E2 ALIGN=MIDDLE  ALT=\"%28x+-+a%29%5E2+%2B+y%5E2+=+a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after changing to rectangular coordinates.<BR>\n" );
document.write( "A direct calculation of the area of this circle using the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A+=+pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "would give the same answer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2pi ALIGN=MIDDLE  ALT=\"a%5E2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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