Homework section 7.5 and 7.6 Trapezoidal Rule and Simpson’s Rule
Problems for this section:
From the book:
Section 7.5 # 9, 11, 22.
Other:
1. Consider R1
0cos(cos(t))dt. Estimate the value of this integral with n= 5 using first the
trapezoidal rule, then using Simpson’s Rule. What is the error bound in each case? Suppose
we want to compute the integral with an error of < .001. What value of nis required for each
of the two methods?
2. Consider R1
0√1 + x3dt. Estimate the value of this integral with n= 5 using first the trape-
zoidal rule, then using Simpson’s Rule. What is the error bound in each case? Suppose we
want to compute the integral with an error of < .001. What value of nis required for each of
the two methods?
3. Consider R1
0
sin(t
tdt. Estimate the value of this integral with n= 5 using first the trapezoidal
rule, then using Simpson’s Rule. What happens at x= 0? What is the error bound in each
case? Suppose we want to compute the integral with an error of < .001. What value of nis
required for each of the two methods?
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