document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=287433>Question 287433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the following integral: The aria bound by the straight line y=x and tha parabola <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=x%5E2 ALIGN=MIDDLE  ALT=\"+y=x%5E2\"   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 #208308 by </B><A HREF=/tutors/aboutme.mpl?userid=nabla><B>nabla(475)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nabla><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=208308\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, find where x=x^2 (this gives the end points of the closed interior). This occurs when 1=x and 0=x. So, we are interested in the closed interval [0,1].\r<BR>\n" );
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document.write( "Now, you will note by graphing that x>=x^2 throughout [0,1]. IE. .5>.25 etc.\r<BR>\n" );
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document.write( "So we integrate from 0 to 1 of (x-x^2)dx.\r<BR>\n" );
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document.write( "This is (x^2/2)  -(x^3/3) evaluated from 0 to 1 so we have (1/2)-(1/3)=1/6.<BR>\n" );
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