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1. Integrate the following: (a) Sx2 vx3 + 5 dx (b) S cos(3x) dx 2. Integrate the following: (a) S x2-2x+1 - dx x+1 (b) S sec2 (3x) dx 3. Integrate the following using the integral tables in http://scidiv.bellevuecollege.edu/dh/Calculus_all/CalculusRefFacts (a) f sec(3x) dx (b) S sin2 (2x) dx 4. Given the two functions y1 = g(x) = x4+ 7x y2 = f(x) =-x (a) Plot the two curves on a graph. (b) What are the two points of intersection of the two functions? (c) Using the area formula A = Self (x) - g(x)]dx to find the area enclosed by the two curves.5. Given the function y = -x2 + 4x (a) Plot the function. (b) Find the area enclosed by y and the x-axis between x = 0 and x = 2 by forming a "center" Riemann sum with Ax - 0.5. Fill in the following table. x interval Xi f(xi) f(xi) Ax number 1: 0-0.5 2: 0.5 - 1.0 3: 1.0 -1.5 4: 1.5 -2.0 (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. https://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)6. Find the area of the ellipse with the equation a2 b2 = 1, or y = Vaz - x2 X = 1 0= 8 X -10 10 -10 10 b= 3 X -10 10 A = 4 So y dx (total area = 4 times the area of a quarter of the ellipse) Use the substitution x = a sin(0) and the trigonometric identities sin2(0) + cos2(0) = 1, cos2(0) = 1/2 + 1/2 cos(20). With the substitution, remember to change the x limits of 0 and a to the equivalent 0 limits