Science:Math Exam Resources/Courses/MATH101/April 2018/Question 01 (iii)
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Question 01 (iii) 

Evaluate . Simplify your answer completely. 
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 

Observe that is an odd function and the integral is over a symmetric interval centered at zero. 
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.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The trick here is to notice that is an odd function (since is an even function and is an odd function) and the integral is over a symmetric interval which is centered at zero. Recall that integrating an odd function over such an interval always gives the value zero, so after applying linearity of the integral this complicated term will disappear and we get Answer: The correct answer is . 