009B Sample Midterm 1, Problem 4

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Evaluate the integral:


Foundations:  
1. Recall the trig identity
       
2. How would you integrate  

        You can use  -substitution.

        Let  
        Then,  
        Thus,

       


Solution:

Step 1:  
First, we write
       
Using the identity  
we get
       
If we use this identity, we have

       

Step 2:  
Now, we use  -substitution.
Let  
Then,  
Therefore,

       


Final Answer:  
       

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