Use the table values and apply the Simpson's Rule to approximate to one decimal place.
A) 1.7
B) 1.6
C) 1.3
D) 2.0
E) 2.3

Question

Use the table values and apply the Simpson's Rule to approximate  to one decimal place. 
A) 1.7 
B) 1.6 
C) 1.3 
D) 2.0 
E) 2.3

Quizplus · Accepted Answer

To use Simpson's Rule, we need to divide the interval into subintervals of equal length. Let's use four subintervals, so each subinterval has a length of 1. From the data, we have:
f(0) = 1.5
f(1) = 2.4
f(2) = 3.5
f(3) = 4.3
f(4) = 5.5
Using Simpson's Rule, the approximation is:
approx = (1/3)(1)(1.5 + 4(2.4) + 2(3.5) + 4(4.3) + 5.5) = 16.7
Rounded to one decimal place, we get 16.7, which is closest to 17 or 2.0. Therefore, the best choice is D, with an explanation that the approximation using Simpson's Rule is 16.7, rounded to 2.0.

Use the Table Values and Apply the Simpson's Rule to Approximate