Science:Math Exam Resources/Courses/MATH101/April 2015/Question 01 (b) (i)
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Question 01 (b) (i) |
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For each integral, choose the substitution type that is most beneficial for evaluating the integral. (Write F, G, or H in each box; each answer will be used exactly once.) F. G. H: (i) |
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. |
Hint 1 |
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Suppose you have an integral of the form , which of the given substitutions will help you to use a trigonometry identity to simplify the denominator into one single function? |
Hint 2 |
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Recall that . |
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
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Solution |
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Please rate my easiness! It's quick and helps everyone guide their studies. We need to see which trigonometric identity will help us in each case. The first step is to get rid of the coefficient of by factoring. . Given that in the denominator we have and compare it with the identity , we conclude that the right choice of substitution is with , because then the denominator changes to , which no longer involves a square root. The right answer is then . |