document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=857703>Question 857703</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the centroid of the area under <BR>\n" );
document.write( "y = 1 + x + {x}^{2}<BR>\n" );
document.write( " from x = 0 to x = 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #516824 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=516824\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first integrate and evaluate y = 1 + x + {x}^2<BR>\n" );
document.write( "x+C +x^2/2 +x^3/3<BR>\n" );
document.write( "Area under curve evaluated for x =0 to 2 is<BR>\n" );
document.write( "2+2+8/3 = 6 2/3<BR>\n" );
document.write( "the centroid of the area is total moments / area<BR>\n" );
document.write( "total moments = integral from x = 0 to 2 of x*f(x)dx<BR>\n" );
document.write( "x*f(x) = x + x^2 + x^3<BR>\n" );
document.write( "now integrate x + x^2 + x^3<BR>\n" );
document.write( "x^2/2 + x^3/3 + x^4/4<BR>\n" );
document.write( "evaluate for x = 0 to 2<BR>\n" );
document.write( "2 + 8/3 + 4 = 8 2/3<BR>\n" );
document.write( "now calculate (8 2/3) / (6 2/3) = (26/3) / (20/3) = (26 * 3) / (20 * 3) =  1.3<BR>\n" );
document.write( "centroid of the area is 1.3<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );