Science:Math Exam Resources/Courses/MATH101/April 2013/Question 05 (a)
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Question 05 (a) 

FullSolution Problems. In questions 4–12, justify your answers and show all your work. If a box is provided, write your final answer there. Unless otherwise indicated, simplification of numerical answers is required in these questions. Using a limit of rightendpoint Riemann sums, evaluate . No credit will be given for the use of antidifferentiation, but you may use it to check your answer. You may use the formulas and . 
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 

The Riemann sum is given by . What should you use for ? 
Hint 2 

The righthand endpoints are given by . 
Hint 3 

The widths of the rectangles in a rectangle Riemann sum is given by . 
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. The widths of the rectangles in a rectangle Riemann sum is given by , and the righthand endpoints are given by . Then using the given formulas, 