A student approximates the area enclosed by the curve for by using Simpson’s rule…
MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration
Problem
A student approximates the area enclosed by the curve r=1+sinθ for 0≤θ≤π by using Simpson’s rule with evenly spaced θ–values. The calculator returns the following results:
n (even) 4 8 16
area 6.812 6.973 7.010
The student wants an approximation within 0.05 square unit of the limiting value of the area. What is the least even value of n shown that meets this requirement?
(a) n=4
(b) n=16
(c) n=8
(d) The accuracy requirement is not met by any of the n values shown.