document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=350700>Question 350700</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation:<BR>\n" );
document.write( "Let R be the region enclosed by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=-%28x-1%29%5E2%2B1+ ALIGN=MIDDLE  ALT=\"+y=-%28x-1%29%5E2%2B1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the x-axis.\r<BR>\n" );
document.write( "\n" );
document.write( "a. Find the area of the region R.<BR>\n" );
document.write( "b. Find the volume of the solid generated by rotating R about the y-axis.<BR>\n" );
document.write( "c. Find the volume of the solid generated by rotating R about the x-axis.<BR>\n" );
document.write( "d. Set up, but DO NOT EVALUATE, a definite integral representing the volume<BR>\n" );
document.write( "of the solid generated by rotating R about x = 2.<BR>\n" );
document.write( "e. Set up, but DO NOT EVALUATE, a definite integral representing the volume<BR>\n" );
document.write( "of the solid generated by rotating R about y = 2.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #250769 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=250769\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=”Garamond” size=”+2”>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Part a):\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ \int_0^2\,\left(-(x\,-\,1)^2\ +\ 1\right)\,dx\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ \int_0^2\,\left(-\left(x^2\,-\,2x\,+\ 1\right)\ +\ 1\right)\,dx\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ -\ \int_0^2\ x^2\,dx\ +\ \int_0^2\ 2x\,dx\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ \left\[-\frac{x^3}{3}\right\]_0^2\ +\ \left\[x^2\right\]_0^2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ -\frac{8}{3}\ +\ 0\ +\ 4\ -\ 0\ =\ \frac{4}{3}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Write back and we can negotiate compensation for the rest of this.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<div  DISABLED_style= \"text-align:center\"><a  rel=nofollow HREF=\"http://outcampaign.org/\" target=\"_blank\"><IMG STYLE=\"max-width:80%;\" src=\"http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png\" border=\"0\" alt=\"The Out Campaign: Scarlet Letter of Atheism\" width=\"143\" height=\"122\" /></a></div><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );