document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019015>Question 1019015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> THIS IS INTEGRAL CALCULUS with ANALYTIC GEOMETRY\r<BR>\n" );
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document.write( "find the area bounded by the curves<BR>\n" );
document.write( "find points of intersections<BR>\n" );
document.write( "lower and upper limit<BR>\n" );
document.write( "the working integral with lower and upper limits<BR>\n" );
document.write( "final answer \r<BR>\n" );
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document.write( "1 f(x)=4-x^2 and g(x)=x+2<BR>\n" );
document.write( "2 f(x)e^x and g(x)=e^-x<BR>\n" );
document.write( "3 f(x)= square root of x and g(x)=x3<BR>\n" );
document.write( "4 f(x)=x^2 and g(x)=-x^2 \r<BR>\n" );
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document.write( "thank you so much i will make this a reviewer. Godbless! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635078 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=635078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) f(x)=4-x^2 and g(x)=x+2<BR>\n" );
document.write( "4 - x^2 = x + 2<BR>\n" );
document.write( "x^2 +x -2 = 0<BR>\n" );
document.write( "(x+2)(x-1) = 0<BR>\n" );
document.write( "x = -2 or x = 1<BR>\n" );
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document.write( "points of intersection are (-2, 0) and (1, 3)<BR>\n" );
document.write( "lower limit is -2 and upper limit is 1<BR>\n" );
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document.write( "consider the graph of the two functions f(x) red line, g(x) green line<BR>\n" );
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document.write( "the area bounded by the curves is found by subtracting the area of the curve below from the area of the curve above, in our case<BR>\n" );
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document.write( "we integrate from -2 to 1 (f(x) - g(x))<BR>\n" );
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document.write( "f(x) - g(x) = 4 - x^2 -x - 2 = -x^2 -x + 2<BR>\n" );
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document.write( "now integrate term by term<BR>\n" );
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document.write( "integral is -x^3/3 -x^2/2 + 2x,  evaluate this for x1=-2 and x2=1<BR>\n" );
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document.write( "(-1/3 -1/2 +2) - (8/3 -4/2 -4) = 7/6 - (-20/6) = 27/6 = 9/2 = 4.5 <BR>\n" );
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document.write( "area is 4.5 square units<BR>\n" );
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document.write( "problems 2 - 4 are found by the same method </SPAN>\n" );
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