Use 6 Trapezoids to estimate Integral

Question

Given the table below for selected values of f(x), use 6 trapezoids to estimate the value of  .

x

1

3

4

6

7

9

10

f(x)

4

8

6

10

10

12

16

Answer 1

∫₁¹⁰f(x)dx ≈ (4 +8)/2·(3 - 1) + (8 + 6)/2·(4 - 3) + (6 + 10)/2·(6 - 4) + (10 + 10)/2·(7 - 6) + (10 + 12)/2·(9 - 7) + (12 + 16)/2·(10 - 9) = 12 + 7 + 16 + 10 + 22 + 14 = 81.

Answer: 81