Practice 1 1. (15 pts) For the function f(x) = 3x2, find a formula for a Riemann sum obtained by dividing the interval [0, 1] into n equal subintervals and using the RIGHT-hand endpoint for each Ck. Then take a limit of these sums as n - co to calculate the area under the curve over [0, 1]. 2. (5 pts) Express the limit lim ER=1 CRAXK, P a partition of [8,11], as a definite integral. 3. Use the Fundamental Theorem of Calculus to: dx a. (5 pts) Find - for y = S V5 + 6t2 dt. b. (5 pts) Find - for y = So V5 + 6t2 dt [ hint: also use the Chain Rule]. 4. Integrate the following indefinite integrals. a. (8 pts) f x1/3 sin(x4/3 + 8) dx b. (7 pts) t3-+5/2 -dt t2 C. (8 pts) | 3y y3 + 1 dy d. (7 pts) tan2 0 sec2 0 de 5. Determine the values of the following definite integrals. a. (10 pts) dx b. (10 pts) S cos 3 2t sin 2t dt c. (10 pts) _ 03(1 + 04)3 de 6. (10 pts) Find the area of the region enclosed by the curves 9x2 + y = 9 and x4 - y = 1. BONUS PROBLEM (8 pts) Evaluate JUST ONE of the following definite integrals. If you try both, you must neatly cross out the one you do not want graded, otherwise neither problem will receive credit. 4/3 3 A. Jo dr 16+9r2 2 B. Je dz z In(z)