MATH105 April 2012
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Question 03 (b)
Evaluate the following definite integral:
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!
Use partial fractions. As a first step you need to factor the denominator.
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One way to evaluate is to use partial fractions.
We note that , and so we decompose the fraction into:
- which becomes
after multiplying through by the common denominator of . If we expand the equation out and find the coefficients of the respective powers of x then:
- From matching the coefficients, so .
- From matching the constant coefficients, which becomes in using the relation above.
This tells us that and therefore .
The integral is easy to evaluate now:
We used the fact that above.
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