Please Help Struggling with Calculus

Question

The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6 trapezoids to approximate the value of the integral from 1 to 2 of f of x, dx . Give 3 decimal places for your answer.

x 1 1.1 1.3 1.6 1.7 1.8 2.0

f(x) 1 3 5 8 10 11 14

Answer 1

f(1) = 1

f(1.1) =3

f(1.3) = 5

f(1.6) = 8

f(1.7) = 10

f(1.8) = 11

f(2) = 14

Trapezoidal Formula:

[f(left) + f(right)]/2 * (right-left)

interval [1, 1.1]: (3 + 1)/2 * (1.1 - 1) = 2 * 0.1 = 0.2

interval [1.1,1.3]: (3 + 5)/2 * (1.3 - 1.1) = 4 * 0.2 = 0.8

interval [1.3,1.6]: (5 + 8)/2 * (1.6 - 1.3) = 6.5 * 0.3 = 1.95

interval [1.6,1.7]: (8 + 10)/2 * (1.7 - 1.6) = 9 * 0.1 = 0.9

interval [1.7,1.8]: (10 + 11)/2 * (1.8 - 1.7) = 10.5 * 0.1 = 1.05

interval [1.8,2.0]: (11 + 14)/2 * (2.0 - 1.8) = 12.5 * 0.2 = 2.5

Total is 7.4