Science:Math Exam Resources/Courses/MATH101/April 2008/Question 01 (d)
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Question 01 (d) 

Write down the Trapezoidal Rule approximation for . Leave your answer expressed as a sum involving cosines. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

The Trapezoid Rule in full generality is

Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Recall that when , , and we have
and that
We plug in these values to see that
completing the question. Note that if we actually compute the value we get that, and that, which already to this low approximation shows fairly good accuracy. 