Science:Math Exam Resources/Courses/MATH103/April 2015/Question 10 (a)
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Question 10 (a) 

Evaluate the 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 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 

Split the integrand into two terms, so that the integral of each term is easier to calculate. 
Hint 2 

Use the substitution . 
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.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Since we can split the integrand into two terms: , it is enough to calculate two integrals and , and combine them.
On the other hand, using the substitution (and hence ), we obtain . Therefore, we get the value of as follows: . 