Science:Math Exam Resources/Courses/MATH105/April 2010/Question 01 (j)
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Question 01 (j) 

Use the trapezoidal rule with to approximate 
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 

What information do we need to do a trapezoidal rule approximation? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. As the hint suggests, we should calculate all the information we need to begin. First, we find the width of the intervals:
We also need the endpoints of the intervals:
Thus the points are 2, 0, 2, and 4. Then the formula for the Trapezoidal rule is
so we can fill in our information:
Notice if we actually evaluate the integral, so we see that the trapezoidal rule with only 4 points is already in fairly good agreement. 