Use Simpson's Rule to approximate with n = 6. Round your answer to two decimal places.
A)7.47
B)14.93
C)39.82
D)13.28
E)39.84

Question

Use Simpson's Rule to approximate  with n = 6. Round your answer to two decimal places. ​
A)7.47 
B)14.93 
C)39.82 
D)13.28 
E)39.84

Quizplus · Accepted Answer

We need to use Simpson's Rule to approximate the integral of the given function with n=6. 
The formula for Simpson's Rule is:

∫a^b f(x)dx ≈ [f(a)+4f((a+b)/2)+f(b)](b-a)/6

Using this formula with a=0, b=2, and n=6:

Δx = (2-0)/6 = 1/3

x0 = 0, x1 = 1/3, x2 = 2/3, x3 = 1, x4 = 4/3, x5 = 5/3, x6 = 2

Summing the function at these points:

f(x0) = f(0) = 0

f(x1) = f(1/3) = 11eb0d3b_98aa_48c0_9790_af41804be403_TB1243_11(1/3) = 3.56

f(x2) = f(2/3) = 11eb0d3b_98aa_48c0_9790_af41804be403_TB1243_11(2/3) = 7.32

f(x3) = f(1) = 11eb0d3b_98aa_48c0_9790_af41804be403_TB1243_11(1) = 13

f(x4) = f(4/3) = 11eb0d3b_98aa_48c0_9790_af41804be403_TB1243_11(4/3) = 23.99

f(x5) = f(5/3) = 11eb0d3b_98aa_48c0_9790_af41804be403_TB1243_11(5/3) = 35.02

f(x6) = f(2) = 11eb0d3b_98aa_48c0_9790_af41804be403_TB1243_11(2) = 42.18

Substituting these values into the Simpson's Rule formula:

∫0^2 11eb0d3b_98aa_48c0_9790_af41804be403_TB1243_11 dx ≈ [0 + 4(3.56) + 2(7.32) + 4(13) + 2(23.99) + 4(35.02) + 42.18](1/3)/6

≈ 14.93

Therefore, the answer is B, 14.93 (rounded to two decimal places).

Use Simpson's Rule to Approximate with N = 6