Science:Math Exam Resources/Courses/MATH101/April 2005/Question 01 (c)
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Question 01 (c) 

If where is a function satisfying , compute 
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 

Apply the fundmental theorem of calculus to the integral 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. By the fundamental theorem of calculus, we know that there exists a function g(x) such that where g(x) is the antiderivative of the function f(x) (i.e: g'(x) = f(x)). Taking the derivative of F(x) gives by the chain rule. Using the antiderivative property of g, Plugging in x = 2 and using the fact that f(4) = 1 gives us our answer 