Question

EASY CHECK MY ANSWER!
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 of f(x) from 1 to 2.

Answer 1

USE THIS TABLE

x 1 1.1 1.3 1.6 1.7 1.8 2.0
f(x) 1 3 5 8 10 11 14

Answer 2

My answer: delta x= (b-a)/n
delta x= (2-1)/6 = 1/6
(1/6)/2 (f(1) + 2f(1.1) + 2f(1.3)+2f(1.6)+2f(1.7)+2f(1.8)+f(2.0))
1/12 (1 + 6 +10 +16+ 20+22+14)
1/12 (89)
89/12 =7.417

Answer 3

@Hero @pooja195

Answer 4

That looks about right, but i prefer to just draw these and do them geometrically (work out the areas of the trapezoids).

Answer 5

btw your answer will be slightly off, because the "height" of each trap. is not 1/6 (the heights vary). Another good reason to just draw it out and do it that way.

Answer 6

That formula for Trapezoidal Rule works only works if the width of your subintervals (i.e. space between two adjacent x-values) are regular.

Answer 7

@mww that's what my last post is saying