Science:Math Exam Resources/Courses/MATH101/April 2012/Question 07 (a)
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Question 07 (a) 

Let . Write down the trapezoidal approximation T_{4} for I. You do not need to simplify your answer. 
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 general formula for the trapezoidal approximation is given by:
What are and ? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The formula for the trapezoidal approximation of the integral is as follows: The 4 of means that our interval of integration has been divided into four pieces, each of length (ba)/4=1/4. So . We also know that and are the endpoints of the interval of integration. So we have
We simply plug this all into the formula given above to get: 