document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119908>Question 1119908</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = -x^3 and y = -x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735603 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=735603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You didn't give limits so I'll make my own.<BR>\n" );
document.write( "You can modify the solution as needed.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=dfp1.JPG\">.<BR>\n" );
document.write( "So find the area between <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;\" > and <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;\" >.<BR>\n" );
document.write( "The four regions are from<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;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.75 ALIGN=MIDDLE  ALT=\"x=-0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BM1%5D=-0.875 ALIGN=MIDDLE  ALT=\"x%5BM1%5D=-0.875\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.75 ALIGN=MIDDLE  ALT=\"x=-0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.5 ALIGN=MIDDLE  ALT=\"x=-0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BM2%5D=-0.625 ALIGN=MIDDLE  ALT=\"x%5BM2%5D=-0.625\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.5 ALIGN=MIDDLE  ALT=\"x=-0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.25 ALIGN=MIDDLE  ALT=\"x=-0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BM3%5D=-0.375 ALIGN=MIDDLE  ALT=\"x%5BM3%5D=-0.375\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.25 ALIGN=MIDDLE  ALT=\"x=-0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BM4%5D=-0.125 ALIGN=MIDDLE  ALT=\"x%5BM4%5D=-0.125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the difference of the functions at the midpoints,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=-x-%28-x%5E3%29=x%5E3-x ALIGN=MIDDLE  ALT=\"D=-x-%28-x%5E3%29=x%5E3-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B1%5D=%28-0.875%29%5E3%2B0.875=0.205078 ALIGN=MIDDLE  ALT=\"D%5B1%5D=%28-0.875%29%5E3%2B0.875=0.205078\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B2%5D=%28-0.625%29%5E3%2B0.625=0.380859 ALIGN=MIDDLE  ALT=\"D%5B2%5D=%28-0.625%29%5E3%2B0.625=0.380859\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B3%5D=%28-0.375%29%5E3%2B0.375=0.322266 ALIGN=MIDDLE  ALT=\"D%5B3%5D=%28-0.375%29%5E3%2B0.375=0.322266\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B4%5D=%28-0.125%29%5E3%2B0.125=0.123047 ALIGN=MIDDLE  ALT=\"D%5B4%5D=%28-0.125%29%5E3%2B0.125=0.123047\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sum the differences and multiply by the step in x <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25 ALIGN=MIDDLE  ALT=\"0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B4%5D=%280.205078%2B0.380859%2B0.322266%2B0.123047%290.25 ALIGN=MIDDLE  ALT=\"A%5B4%5D=%280.205078%2B0.380859%2B0.322266%2B0.123047%290.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B4%5D=1.03125%280.25%29 ALIGN=MIDDLE  ALT=\"A%5B4%5D=1.03125%280.25%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%5B4%5D=0.257 ALIGN=MIDDLE  ALT=\"A%5B4%5D=0.257\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );