Question: 5. (10 points) Given the function y = -x3 + 2x2 + 3x (a) Plot the function. (b) Find the area enclosed by y and

5. (10 points) Given the function y = -x3 + 2x2 + 3x (a) Plot the function. (b) Find the area enclosed by y and the xaxis between x = 0 and x = 3 by forming a \"center\" Riemann sum with Ax = 1. Fill in the following table. x interval Xi f(xi) f(xi) Ax number 1: 0 l .5 2: l 2 1.5 3: 2 3 2.5 (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. https:l/WWW.mathauditor.com/simpsonsrule-calcu1ator.html (e) What is the value of the enclosed area if you integrate the function between 0 and 3? (1) Are your three computed areas \"close\"? (yes or no)

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