Trapazoidal rule

Question

My daughter has tried this question and looked at one similar and get get the correct answer. Can anyone show us how to work it? Thanks.

Use the trapezodial rule with n=8 to approximate the integral 1 to 6 (cos(x)/x)dx

Answer 1

This really is onerous busy work! I can tell you how to do it...but I will not do the calculations for you.

Call f(x)=[cos(x)]/x

You need 8 intervals; that means 9 abscissas (values for x)

Δx=5/8 and the abscissas are 1, 1.625, 2.375 and so forth up to 6

Calculate the value of [cos(x)]/x at each abscissa.

Then the answer is the sum f(1)+f(6)+2[f(1.625)+f(2.375)+...+f(5.375)] all multiplied by 5/8.

Good luck!