document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=345463>Question 345463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: Prove the inequality without evaluating the integral. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+pi%2F12+%3C=+int+%28+cos%28x%29%2C+dx%2C+pi%2F6%2C+pi%2F3+%29+%3C=+sqrt%283%29pi%2F12+ ALIGN=MIDDLE  ALT=\"+pi%2F12+%3C=+int+%28+cos%28x%29%2C+dx%2C+pi%2F6%2C+pi%2F3+%29+%3C=+sqrt%283%29pi%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #247117 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=247117\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The value of the cosine function at the endpoints are,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F6%29=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"cos%28pi%2F6%29=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F3%29=1%2F2 ALIGN=MIDDLE  ALT=\"cos%28pi%2F3%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The value of the function in between the endpoints is bounded by those values.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%3C=cos%28x%29%3C=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"1%2F2%3C=cos%28x%29%3C=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then integrating,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29%2Aint%281%2Cdx%2Cpi%2F6%2Cpi%2F3%29+%3C=+int+%28+cos%28x%29%2C+dx%2C+pi%2F6%2C+pi%2F3+%29+%3C=+%28sqrt%283%29%2F2%29%2Aint%281%2Cdx%2Cpi%2F6%2Cpi%2F3%29++ 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=+%281%2F2%29%28pi%2F3-pi%2F6%29+%3C=+int+%28+cos%28x%29%2C+dx%2C+pi%2F6%2C+pi%2F3+%29+%3C=+%28sqrt%283%29%2F2%29%28pi%2F3-pi%2F6%29+ 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=pi%2F3-pi%2F6=%282pi%29%2F6-pi%2F6=pi%2F6 ALIGN=MIDDLE  ALT=\"pi%2F3-pi%2F6=%282pi%29%2F6-pi%2F6=pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29%28pi%2F6%29+%3C=+int+%28+cos%28x%29%2C+dx%2C+pi%2F6%2C+pi%2F3+%29+%3C=+%28sqrt%283%29%2F2%29%28pi%2F6%29+ 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=+highlight%28pi%2F12+%3C=+int+%28+cos%28x%29%2C+dx%2C+pi%2F6%2C+pi%2F3+%29+%3C=+%28sqrt%283%29%2F12%29pi%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );