Question: 5. (10 points) Given the function y = -x2 + 4x (a) Plot the function. (b) Find the area enclosed by y and the xaxis

5. (10 points) Given the function y = -x2 + 4x (a) Plot the function. (b) Find the area enclosed by y and the xaxis between x = 0 and x = 2 by forming a \"center\" Riemann sum with Ax = 0.5. Fill in the following table. x interval number 1: 00.5 2: 0.5 1.0 3: 1.0 1.5 4: 1.52.0 (c) What is your estimate of the enclosed area from the Riemann sum? (d) What is your estimate of the enclosed area if you use Simpson's rule? Include a screen shot of your answer. ht_tps://Www.mathauditor.com/Simpsons-rule-calculator.html (e) What is the value of the enclosed area if you integrate the function between 0 and 2? (f) Are your three computed areas \"close\"? (yes or no)

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