MATH 140A.2/4 Name:MATH 140A.2/4 Name:Quiz#9 SSN:11-21-2003Total = 30 points. Show all your work! Find the following indefinite integrals, check the correctness of your answer by differentiation.1. (4x + 1)2 dx2. (9x4/5 + 5x1/3 + π) dx 3. tan2(2x) dx4. cos2(4) d5. Suppose y = 6 – cos(x), y(0) = 4 and y(0) = 2, find y.(continue)6. What is the area of the largest rectangle which can be inscribed in the ellipse x2/9 + y2/16 = 1? (Hint: The problem is easier to solve by substituting x = 3cos() and y = 4sin(), and find the optimal angle that would maximize the area.) 7. After more evil-doings, Mojo Jojo is fleeing east away from (the ruin of) Townsville at5 miles per minute. Heading north at a speed of 15 miles per minute toward Townsville are the trio of kindergartener-superheroes: Blossom, Bubbles, and Buttercup. How fast isthe distance between Mojo Jojo and the Powerpuff Girls changing at the moment when Mojo is 12 miles away and PPGs are 5 miles from
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