document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029355>Question 1029355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the Fundamental Theorem to evaluate the integral from 0 to 3 of the quantity x cubed minus 6 times x, dx.<BR>\n" );
document.write( "(Your answer must include the antiderivative.) \r<BR>\n" );
document.write( "\n" );
document.write( "Use a graph of the function to explain the geometric meaning of the value of the integral. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644401 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=644401\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%28x%5E3-6x%29%2Cdx%29=x%5E4%2F4-3x%5E2%2BC ALIGN=MIDDLE  ALT=\"int%28%28x%5E3-6x%29%2Cdx%29=x%5E4%2F4-3x%5E2%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Evaluated,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%28x%5E3-6x%29%2Cdx%2C0%2C3%29=%283%5E4-0%5E4%29%2F4-3%283%5E2-0%5E2%29 ALIGN=MIDDLE  ALT=\"int%28%28x%5E3-6x%29%2Cdx%2C0%2C3%29=%283%5E4-0%5E4%29%2F4-3%283%5E2-0%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%28x%5E3-6x%29%2Cdx%2C0%2C3%29=81%2F4-27 ALIGN=MIDDLE  ALT=\"int%28%28x%5E3-6x%29%2Cdx%2C0%2C3%29=81%2F4-27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%28x%5E3-6x%29%2Cdx%2C0%2C3%29=81%2F4-108%2F4 ALIGN=MIDDLE  ALT=\"int%28%28x%5E3-6x%29%2Cdx%2C0%2C3%29=81%2F4-108%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%28x%5E3-6x%29%2Cdx%2C0%2C3%29=-27%2F4 ALIGN=MIDDLE  ALT=\"int%28%28x%5E3-6x%29%2Cdx%2C0%2C3%29=-27%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=x3.JPG\">.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The integral is equal to the area of the curve, below the x-axis is negative, above the x-axis is positive. <BR>\n" );
document.write( "Since more area is below the x-axis, the total area is negative.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );