Science:Math Exam Resources/Courses/MATH101 A/April 2024/Question 01
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Question 01 |
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Find , given |
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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What does the fundamental theorem of calculus say? Note that the upper bound of the integral defining is , not . |
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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One version of the fundamental theorem of calculus is In our case, is a composite of the two functions
We wish to apply the chain rule. The derivatives are
so we have
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