Science:Math Exam Resources/Courses/MATH101 A/April 2024/Question 04
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Question 04 |
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Evaluate |
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 |
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Try making a substitution that simplifies the exponent in the trigonometric function, and rewrite the simplified integral accordingly. |
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.
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Solution |
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We simplify the integral by the following substitution; let , so Using this substitution, the integration bounds can be rewritten in terms of as follows:
Then we have
Note that there is no constant of integration in a definite integral. |