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170 Part IV: Integration and Infinite Series
15. Continuing with problem 4, estimate the 16. Estimate the same area as problem 15 with
area under y = sinx from 0 to π with 8 16 and 24 trapezoids and compute the per-
trapezoids, and compute the percent error. cent errors.
Solve It Solve It
17. Approximate the same area as problem 15 18. Use the following shortcut to figure S 20 for
with 8 Simpson’s rule “trapezoids” and the area under lnx from 1 to 6. (Use the
compute the percent error. results from problem 2 and the first exam-
ple in this section.)
Solve It
Shortcut: If you know the midpoint and
trapezoid estimates for n rectangles, you
can easily compute the Simpson’s rule esti-
mates for n curvy-topped “trapezoids” with
the following formula:
M n + M n + T n
S n2 =
3
Solve It
