Use the Trapezoidal Rule to approximate with n = 6. Round your answer to two decimal places.
A) 1091.56
B) 323.56
C) 545.78
D) 212.44
E) 444.44

Question

Use the Trapezoidal Rule to approximate  with n = 6. Round your answer to two decimal places. ​
A) 1091.56 
B) 323.56 
C) 545.78 
D) 212.44 
E) 444.44

Quizplus · Accepted Answer

Using the Trapezoidal Rule, we have:

h = (b-a)/n = (1-0)/6 = 1/6
x1 = 0
x2 = 1/6
x3 = 2/6
x4 = 3/6
x5 = 4/6
x6 = 5/6

f(x1) = 11
f(x2) = 11.14
f(x3) = 11.39
f(x4) = 11.67
f(x5) = 11.96
f(x6) = 12.25

Using the formula:

∫f(x)dx ≈ (h/2)[ f(x0) + 2∑f(xi) + f(xn) ]

where x0 = a and xn = b,

we get:

∫11ea984b_b10e_39fc_9029_edd425b9a556_TB4005_11 dx ≈ (1/12)[ 11 + 2(11.14+11.39+11.67+11.96) + 12.25 ] = 545.78

Rounding to two decimal places, we get 545.78, which corresponds to choice C.

Use the Trapezoidal Rule to Approximate with N =