(10 points) Use the error formulas to find bounds for the error when
\int_0 (1)/(x+1)dx
is approximated using the trapezoid rule and Simpson's rule with
n=6
. (The error formulas are given below.) Using the trapezoid rule gives an error of at most Using Simpson's rule gives an error of at most The errors
E
in approximating
\int_a^b f(x)dx
are: Trapezoid rule:
|E|<=((b-a)^(3))/(12n^(2))[max|f^('')(x)|],a<=x<=b
Simpson's rule:
|E|<=((b-a)^(5))/(180n^(4))[max|f^((4))(x)|],a<=x<=b

Question

(10 points) Use the error formulas to find bounds for the error when

\int_0 (1)/(x+1)dx

is approximated using the trapezoid rule and Simpson's rule with

n=6

. (The error formulas are given below.) Using the trapezoid rule gives an error of at most Using Simpson's rule gives an error of at most The errors

E

in approximating

\int_a^b f(x)dx

are: Trapezoid rule:

|E|<=((b-a)^(3))/(12n^(2))[max|f^('')(x)|],a<=x<=b

Simpson's rule:

|E|<=((b-a)^(5))/(180n^(4))[max|f^((4))(x)|],a<=x<=b

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