document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=350018>Question 350018</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: Sketch the regions enclosed by the given curves and then find the area of the regions.\r<BR>\n" );
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document.write( "a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=e%5Ex+ ALIGN=MIDDLE  ALT=\"+y=e%5Ex+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=%28x-1%29%5E2+ ALIGN=MIDDLE  ALT=\"+y=%28x-1%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <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;\" >\r<BR>\n" );
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document.write( "b. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=-7-x%2B3x%5E2+ ALIGN=MIDDLE  ALT=\"+y=-7-x%2B3x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=2x-x%5E2+ ALIGN=MIDDLE  ALT=\"+y=2x-x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=1=cosx+ ALIGN=MIDDLE  ALT=\"+y=1=cosx+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=cosx+ ALIGN=MIDDLE  ALT=\"+y=cosx+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0%3C=x%3C=pi+ ALIGN=MIDDLE  ALT=\"+0%3C=x%3C=pi+\"   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 #250218 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=250218\">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=graph%28300%2C300%2C-2%2C4%2C-2%2C4%2Ce%5E%28x%29%2C%28x-1%29%5E2%2C2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C4%2C-2%2C4%2Ce%5E%28x%29%2C%28x-1%29%5E2%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the intersection point between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=e%5Ex ALIGN=MIDDLE  ALT=\"y=e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex=2 ALIGN=MIDDLE  ALT=\"e%5Ex=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=ln%282%29 ALIGN=MIDDLE  ALT=\"x=ln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then the area would be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=int%28%28e%5E%28x%29-%28x-1%29%5E2%29%2Cdx%2C0%2Cln%282%29%29%2Bint%28%282-%28x-1%29%5E2%29%2Cdx%2Cln%282%29%2C1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Expand the terms, integrate, and simplify to get the final answer.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-7-x%2B3x%5E2%2C2x-x%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-7-x%2B3x%5E2%2C2x-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Same procedure. <BR>\n" );
document.write( "Find the two intersection points <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x1 ALIGN=MIDDLE  ALT=\"x1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x2 ALIGN=MIDDLE  ALT=\"x2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by solving,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7-x%2B3x%5E2=2x-x%5E2 ALIGN=MIDDLE  ALT=\"-7-x%2B3x%5E2=2x-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Proceed as above integrating from one intersection point to the other.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=int%28%28-7-x%2B3x%5E2-2x%2Bx%5E2%29%2Cdx%2Cx1%2Cx2%29=int%28%284x%5E2-3x-7%29%2Cdx%2Cx1%2Cx2%29 ALIGN=MIDDLE   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/plot-formula.mpl?expression=graph%28300%2C300%2C-1%2C4%2C-3%2C3%2C1%2Bcos%28x%29%2C1-cos%28x%29%2Ccos%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1%2C4%2C-3%2C3%2C1%2Bcos%28x%29%2C1-cos%28x%29%2Ccos%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'm not sure if the first function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bcos%28x%29 ALIGN=MIDDLE  ALT=\"1%2Bcos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-cos%28x%29 ALIGN=MIDDLE  ALT=\"1-cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If it's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bcos%28x%29 ALIGN=MIDDLE  ALT=\"1%2Bcos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the integration is straightforward since<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bcos%28x%29-cos%28x%29=1 ALIGN=MIDDLE  ALT=\"1%2Bcos%28x%29-cos%28x%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Integrating that over <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;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=pi ALIGN=MIDDLE  ALT=\"x=pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > would give you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28pi-0%29=pi ALIGN=MIDDLE  ALT=\"A=%28pi-0%29=pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If it's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-cos%28x%29 ALIGN=MIDDLE  ALT=\"1-cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then find the intersection point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x1 ALIGN=MIDDLE  ALT=\"x1\"   DISABLED_style= \"max-width:90%; height:auto;\" > again where,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-cos%28x%29=cos%28x%29 ALIGN=MIDDLE  ALT=\"1-cos%28x%29=cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then you have to modify the area because at this point the functions cross.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=int%28%281-2cos%28x%29%29%2Cdx%2C0%2Cx1%29%2Bint%28%282cos%28x%29-1%29%2Cdx%2Cx1%2Cpi%29 ALIGN=MIDDLE  ALT=\"A=int%28%281-2cos%28x%29%29%2Cdx%2C0%2Cx1%29%2Bint%28%282cos%28x%29-1%29%2Cdx%2Cx1%2Cpi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );