document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=302713>Question 302713</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please Help,<BR>\n" );
document.write( "Estimate the area under the curve { { { f(x)= -x^2+4x+4.25 over 0 <= x <= 5 } } } . Use 5 intervals. \r<BR>\n" );
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document.write( "I tried to graph it on a graphing calculator first, but I think it was wrong because I can't enter 0 <= x <= 5. Here is the link of the graphed equation: http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html \r<BR>\n" );
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document.write( "Thanks for the help :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #217031 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=217031\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You didn't specify a method. <BR>\n" );
document.write( "Break up the area into 5 regions.<BR>\n" );
document.write( "Calculate an average value of f(x) and the right and left endpoint. <BR>\n" );
document.write( "Then multiply the average value of f(x) by dx in each region. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=0 ALIGN=MIDDLE  ALT=\"+x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%280%29=4.25 ALIGN=MIDDLE  ALT=\"+f%280%29=4.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=1 ALIGN=MIDDLE  ALT=\"+x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%281%29=7.25 ALIGN=MIDDLE  ALT=\"+f%281%29=7.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=2 ALIGN=MIDDLE  ALT=\"+x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%282%29=8.25 ALIGN=MIDDLE  ALT=\"+f%282%29=8.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=3 ALIGN=MIDDLE  ALT=\"+x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%283%29=7.25 ALIGN=MIDDLE  ALT=\"+f%283%29=7.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=4 ALIGN=MIDDLE  ALT=\"+x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%284%29=4.25 ALIGN=MIDDLE  ALT=\"+f%284%29=4.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=5 ALIGN=MIDDLE  ALT=\"+x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%285%29=-0.75 ALIGN=MIDDLE  ALT=\"+f%285%29=-0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "SO then area 1 equals,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A1=%281%2F2%29%28f%280%29%2Bf%281%29%29%2A%281-0%29=5.75+ ALIGN=MIDDLE  ALT=\"A1=%281%2F2%29%28f%280%29%2Bf%281%29%29%2A%281-0%29=5.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A2=%281%2F2%29%28f%281%29%2Bf%282%29%29%2A%282-1%29=7.75 ALIGN=MIDDLE  ALT=\"A2=%281%2F2%29%28f%281%29%2Bf%282%29%29%2A%282-1%29=7.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A3=%281%2F2%29%28f%282%29%2Bf%283%29%29%2A%283-2%29=7.75 ALIGN=MIDDLE  ALT=\"A3=%281%2F2%29%28f%282%29%2Bf%283%29%29%2A%283-2%29=7.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A4=%281%2F2%29%28f%283%29%2Bf%284%29%29%2A%284-3%29=5.75 ALIGN=MIDDLE  ALT=\"A4=%281%2F2%29%28f%283%29%2Bf%284%29%29%2A%284-3%29=5.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A5=%281%2F2%29%28f%284%29%2Bf%285%29%29%2A%285-4%29=1.75 ALIGN=MIDDLE  ALT=\"A5=%281%2F2%29%28f%284%29%2Bf%285%29%29%2A%285-4%29=1.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Atot=A1%2BA2%2BA3%2BA4%2BA5=28.75 ALIGN=MIDDLE  ALT=\"Atot=A1%2BA2%2BA3%2BA4%2BA5=28.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The exact value is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29.583 ALIGN=MIDDLE  ALT=\"29.583\"   DISABLED_style= \"max-width:90%; height:auto;\" > so that's a pretty good approximation (within 3%). <BR>\n" );
document.write( " </SPAN>\n" );
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