document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1130687>Question 1130687</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Region R is bounded by the  curve y = x^2 + 2 and the line y = 6 - x^2  . Find intersection point between two graph and area of R. Sketch the graph. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747362 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=747362\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = x^2 + 2 = f(x)<BR>\n" );
document.write( "y = 6 - x^2 = g(x)<BR>\n" );
document.write( "Adding the two equations, we get 2y = 8 -> y = 4<BR>\n" );
document.write( "Solve for x:<BR>\n" );
document.write( "4 = x^2 + 2 -> x = +-sqrt(2)<BR>\n" );
document.write( "The area bounded by the two curves is given by the integral of the difference<BR>\n" );
document.write( "between g(x) and f(x) from -sqrt(2) and sqrt(2).<BR>\n" );
document.write( "I will leave that as an exercise for you to determine the integral.\r<BR>\n" );
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