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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 27 "The Area between Two Curv
es" }}{PARA 0 "" 0 "" {TEXT -1 55 "Example 1.  Find the area enclosed \+
by y=f(x) and y=g(x)" }}{PARA 0 "" 0 "" {TEXT -1 197 "Solution:   The \+
first step in a problem which involves finding the area bounded betwee
n two curves is to plot the graph of the two curves simultaneously.  U
sing Maple V we define the two functions." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "f := x -> 4 - x^2;  g := x->exp(x);" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 36 "Now plot both curves simultaneously." }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 36 "plot(\{f(x),g(x)\},x=-5..5,y=-10..10);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "sol := fsolve(\{y=f(x),y=g
(x)\},\{x,y\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "a:=fsolv
e(f(x)-g(x)=0,x,-3..0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "
b:=fsolve(f(x)-g(x)=0,x,0..3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
176 "Observe that the points of intersection have coordinates given by
  (-1,3),  and  (3,-5), which agrees with the previous hand calculatio
n.  The value of the integral is given by" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "Int(f(x)-g(x),x=a..b);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Exam
ple 2. Find the area of bounded by  x=cos(y) and  x=cos(2*y)." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "implicitplot(\{x=cos(y),x=2*cos(y)
\},x=-1..2,y=-Pi..Pi);" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 35 "Int(2*cos(y)-cos(y),y=-Pi/2..Pi/2);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 158 "
Remark: Of course if we write x=y in the question above, we get an are
a between y=cos(x) and y=2*cos(x), which will use 'vertical' rectangle
 to find the area." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK 
"15" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }