document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1041431>Question 1041431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Reverse the order of integration of the following integral, then calculate it:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"https://i.imgsafe.org/d54d2471df.png\"> </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #656399 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=656399\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The region of integration is the right half of the parabolic region (or to the right of the y-axis.)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+200%2C+-2%2C+2%2C+0%2C+4%2C+4-x%5E2+%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+200%2C+-2%2C+2%2C+0%2C+4%2C+4-x%5E2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28+int+%28%28xe%5E%282y%29%29%2F%284-y%29%2C+dy%2C0%2C4-x%5E2%29%2Cdx%2C0%2C2++%29 ALIGN=MIDDLE  ALT=\"int%28+int+%28%28xe%5E%282y%29%29%2F%284-y%29%2C+dy%2C0%2C4-x%5E2%29%2Cdx%2C0%2C2++%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28+int+%28%28xe%5E%282y%29%29%2F%284-y%29%2C+dx%2C0%2Csqrt%284-y%29%29%2Cdy%2C0%2C4++%29 ALIGN=MIDDLE  ALT=\"int%28+int+%28%28xe%5E%282y%29%29%2F%284-y%29%2C+dx%2C0%2Csqrt%284-y%29%29%2Cdy%2C0%2C4++%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "(In the inner integral, I integrated wrt x only from 0 to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284-y%29 ALIGN=MIDDLE  ALT=\"sqrt%284-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, as per the region of integration.)\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28+%28e%5E%282y%29%2F%284-y%29%29%2Aint%28x%2C+dx%2C0%2Csqrt%284-y%29%29%2Cdy%2C0%2C4+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28+%28e%5E%282y%29%2F%284-y%29%29%2A%28x%5E2%2F2%290%5Esqrt%284-y%29%2Cdy%2C0%2C4+%29 ALIGN=MIDDLE  ALT=\"int%28+%28e%5E%282y%29%2F%284-y%29%29%2A%28x%5E2%2F2%290%5Esqrt%284-y%29%2Cdy%2C0%2C4+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2Aint%28+%28e%5E%282y%29%2F%284-y%29%29%2A%284-y%29%2Cdy%2C0%2C4+%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2Aint%28+%28e%5E%282y%29%2F%284-y%29%29%2A%284-y%29%2Cdy%2C0%2C4+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2Aint%28+e%5E%282y%29%2Cdy%2C0%2C4+%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2Aint%28+e%5E%282y%29%2Cdy%2C0%2C4+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%28e%5E%282y%29%290%5E4 ALIGN=MIDDLE  ALT=\"%281%2F4%29%28e%5E%282y%29%290%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%28e%5E8+-+1%29 ALIGN=MIDDLE  ALT=\"%281%2F4%29%28e%5E8+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );