document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=771777>Question 771777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bowl is designed by revolving completely the area enclosed by y = x^2- 1, y = 3 and x &#8805; 0 around the axis. What is the volume of this bowl? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #470485 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=470485\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\ =\ x^2\ -\ 1\"> is a parabola with vertex at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (0,\,-1)\">.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\ =\ 3\"> is the horizontal line that passes through <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (0,\,3)\"> and that intersects the parabola, in the desired interval, at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (2,\,3)\">.\r<BR>\n" );
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document.write( "It will be convenient to write <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> as a function of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ y\ =\ x^2\ -\ 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ x\ =\ \sqrt{y\ +\ 1}\">\r<BR>\n" );
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document.write( "Rotate the parabola, then consider a thin disk with radius <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{y\ +\ 1}\">.  The volume of this disk is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \pi\left(\sqrt{y\ +\ 1}\right)^2\,dy\ =\ \pi(y\ +\ 1)\,dy\">\r<BR>\n" );
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document.write( "Integrate from -1 to 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \pi\,\int_{-1}^3\,y\ +\ 1\,dy\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \pi\left|\frac{y^2}{2}\ +\ y\right|^3_{-1}\  =\ \pi\left(\left(\frac{9}{2}\ +\ 3\right)\ -\ \left(\frac{-1}{2}\ +\ (-1)\right)\right)\ =\ 9\pi\">\r<BR>\n" );
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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" );
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