Science:Math Exam Resources/Courses/MATH103/April 2013/Question 08 (b)
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Question 08 (b) 

Fundamental Theorem of Calculus Evaluate and simplify . 
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 

This is a one liner. 
Hint 2 

What does an integral give you? What is this derivative? 
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 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. Since integrals give you areas, which are just constants, the derivative of a constant is 0. 
Solution 2 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. For a more convoluted solution, notice that via the FTC, we have . 
Solution 3 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Another convoluted solution: recall the Fundamental Theorem of Calculus in its general form:
Then
