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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Numerical integrations" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f:=x->exp(-x^2);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(f(x),x=-1..1);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 28 "trapezoid(f(x), x=-1..1,10);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 33 "evalf(rightsum(f(x),x=-1..1,10));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "evalf(middlesum(f(x),x=-1..1,10));
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "simpson(f(x),x=-1..1,10
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "evalf(int(f(x),x=-1..1));" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 159 "Remark: For this problem, the sim
pson's rule gives the best approximation when n = 10 is used; middlesu
m is second and trapezoid is the worst. Do you know why?" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 217 "Question:
 For the function g defined below for x in [0.01, 0.1]. Use n=20, and \+
compare the efficiency of using middlesum, trapezoid and Simpson's met
hod. Can you conjecture your answer before you run the program? Why?" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "g:=x->1/x;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(g(x),x=0.1..1);" }}}{EXCHG 
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