document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025589>Question 1025589</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the VOLUME of the solid generated by revolving the region described about the indicated axis.\r<BR>\n" );
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document.write( "1. The region bounded by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3x+-+x%5E2+ ALIGN=MIDDLE  ALT=\"+y+=+3x+-+x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0+ ALIGN=MIDDLE  ALT=\"+y+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > revolved about the x-axis\r<BR>\n" );
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document.write( "2. The region bounded by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+x%5E3+ ALIGN=MIDDLE  ALT=\"+y+=+x%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0+ ALIGN=MIDDLE  ALT=\"+y+=+0+\"   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;\" > revolved about the line <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( "3. The region bounded by <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;\" > and the x-axis revolved about the line <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;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #640891 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=640891\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+int%281%2C+dV%2C+0%2C3%29+=+int%28pi%2Ar%5E2%2C+dx%2C+0%2C3%29+=+pi%2Aint%28%283x+-+x%5E2%29%5E2%2C+dx%2C+0%2C3%29+=+pi%2Aint%28%289x%5E2+-+6x%5E3+%2B+x%5E4%29%2C+dx%2C+0%2C3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> The antiderivative is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E3-%283x%5E4%29%2F2+%2B+x%5E5%2F5 ALIGN=MIDDLE  ALT=\"3x%5E3-%283x%5E4%29%2F2+%2B+x%5E5%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> The volume is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%283%2A3%5E3+-+%283%2F2%29%2A3%5E4+%2B+3%5E5%2F5+%29=+%2881pi%29%2F10 ALIGN=MIDDLE  ALT=\"pi%2A%283%2A3%5E3+-+%283%2F2%29%2A3%5E4+%2B+3%5E5%2F5+%29=+%2881pi%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+int%281%2C+dV%2C+0%2C8%29+=+int%28pi%2Ar%5E2%2C+dy%2C+0%2C8%29+=+pi%2Aint%28%282-y%5E%281%2F3%29%29%5E2%2C+dy%2C+0%2C8%29+=+pi%2Aint%28%284+-+4%2Ay%5E%281%2F3%29+%2B+y%5E%282%2F3%29%29%2C+dy%2C+0%2C8%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> The antiderivative is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y+-+3y%5E%284%2F3%29+%2B+%283%2F5%29%2Ay%5E%285%2F3%29 ALIGN=MIDDLE  ALT=\"4y+-+3y%5E%284%2F3%29+%2B+%283%2F5%29%2Ay%5E%285%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> The volume is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%284%2A8+-+3%2A8%5E%284%2F3%29+%2B%283%2F5%29%2A8%5E%285%2F3%29%29=+%2816pi%29%2F5 ALIGN=MIDDLE  ALT=\"pi%2A%284%2A8+-+3%2A8%5E%284%2F3%29+%2B%283%2F5%29%2A8%5E%285%2F3%29%29=+%2816pi%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I leave the last one to you. </SPAN>\n" );
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