document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003297>Question 1003297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the midpoint riemann sum for f(x) = cos(2x) on the partition <BR>\n" );
document.write( "P = {-pi/2,0,pi/3,pi/2} \r<BR>\n" );
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document.write( "Please show how this is done<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620266 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=620266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First sketch f(x) on the xy-plane and label the points (-pi/2, 0), (0,0), (0, pi/3), and (0,pi/2) (corresponding to the points in P).\r<BR>\n" );
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document.write( "To approximate the integral using the midpoint Riemann sum, for each \"interval\" bounded by consecutive points in P, take the midpoint and evaluate f at that x-value. This becomes your \"height\" of the rectangle. Multiply by the width of the interval.\r<BR>\n" );
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document.write( "For example, for the interval bounded by -pi/2, 0, we would want to take -pi/4 and compute f(-pi/4). Then we multiply f(-pi/4) by pi/2 (the width of the interval). Repeat for the other intervals and add. </SPAN>\n" );
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