document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181931>Question 1181931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate the line integral ∫F⋅dr where F=⟨−3sin(x),−3cos(y),xz⟩ and C is the path given by r(t)=(2t^3,3t^2,−3t) for 0≤t≤1<BR>\n" );
document.write( "∫F⋅dr= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813158 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=813158\">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=x+=+2t%5E3 ALIGN=MIDDLE  ALT=\"x+=+2t%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3t%5E2 ALIGN=MIDDLE  ALT=\"y+=+3t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+-3t ALIGN=MIDDLE  ALT=\"z+=+-3t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28t%29+=+%28matrix%281%2C3%2C+2t%5E3%2C+3t%5E2%2C+-3t%29%29 ALIGN=MIDDLE  ALT=\"r%28t%29+=+%28matrix%281%2C3%2C+2t%5E3%2C+3t%5E2%2C+-3t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dr%28t%29+=+%28matrix%281%2C3%2C6t%5E2%2C6t%2C-3%29%29dt ALIGN=MIDDLE  ALT=\"dr%28t%29+=+%28matrix%281%2C3%2C6t%5E2%2C6t%2C-3%29%29dt\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int+%28F%2Cdr%2C+%28matrix%281%2C3%2C0%2C0%2C0%29%29%2C%28matrix%281%2C3%2C2%2C3%2C-3%29%29%29+=+int%28+%28matrix%281%2C3%2C-3sin%282t%5E3%29%2C+-3cos%283t%5E2%29%2C+-6t%5E4%29%29%2A%28matrix%281%2C3%2C+6t%5E2%2C+6t%2C+-3%29%29%2C+dt%2C+0%2C+1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28-18t%5E2sin%282t%5E3%29-18tcos%283t%5E2%29%2B18t%5E4%2C+dt%2C0%2C1%29 ALIGN=MIDDLE  ALT=\"int%28-18t%5E2sin%282t%5E3%29-18tcos%283t%5E2%29%2B18t%5E4%2C+dt%2C0%2C1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18%2Aint%28t%5E2sin%282t%5E3%29%2Cdt%2C0%2C1%29-18%2Aint%28tcos%283t%5E2%29%2Cdt%2C0%2C1%29%2B+18%2Aint%28t%5E4%2C+dt%2C0%2C1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2Aint%28sin%282t%5E3%29%2Cd%282t%5E3%29%2C0%2C1%29-3%2Aint%28cos%283t%5E2%29%2Cd%283t%5E2%29%2C0%2C1%29%2B+18%2Aint%28t%5E4%2C+dt%2C0%2C1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%28-cos%282t%5E3%29%29%5B0%5D%5E1+-+3%28sin%283t%5E2%29%29%5B0%5D%5E1+%2B+%2818%2F5%29%2A%28t%5E5%29%5B0%5D%5E1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3cos2-3sin3+%2B+3%2F5 ALIGN=MIDDLE  ALT=\"3cos2-3sin3+%2B+3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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