MAC 2312 Midterm: MAC 2312 FIU Exam 113k
15 Feb 2019
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Prof. s. hudson: (5pts each) compute each sum, using a summation formula if possible. Simplify, within reason (fractions are ok, but do not leave a p symbol, or many + signs in your answers). 1 k+1 k 1 k=1 |10 k| P20: (5pts each) compute each integral (by substitution, geometry, ftc, inv. trig, etc): If f (x) = x2 on [a, b], then f (b) f (a) = (b3 a3)/3. The function f (x) = 1/x is integrable on [1, 3]. The function f (x) = cot(x) is integrable on [0, 1]. The displacement of a particle is always nonnegative. (f + g)ave = fave + gave. If possible, use sentences or formulas with complete justi - cations. Bonus: (5 points, maybe hard): find the value of the riemann sum for r 5. 2 3x + 1 dx using the midpoint rule with 2013 subintervals of equal length. If you use any shortcuts, explain your reasoning.
