1. Evaluate sexin(2) d.c. Show your work. 2. Prove that for all p...

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1. Evaluate sexin(2) d.c. Show your work. 2. Prove that for all positive integers n = 1,2,3, we have n 1 1 j(j+1) n + 1 j=1 3. Use a Riemann sum to find the area of the trapezoid bounded by the lines y = 0, x = 1, x = 2, and y = x. See Figure 1. (2,2) y=x y (1,1) X (0,0) X=1 X=2 FIGURE 1. A trapezoid. 4. The friends of a popular tour guide, Chris, estimate that, during the standard eight hour tour, Chris smiles at the rate of smiles (30 + 107 cos (t)) hour '. at time t (in hours) in the range OHow many times does Chris smile on the standard tour between hours 2 and 5? 5. Find the area beneath the curve y = recos(x) and above the curve y = (x - sin(x)) ecos(x) over the range 0 < x < TT. See Figure 2. 3 COSCA y= X e 2 1 N (II, II e \ cos(s) (0,0) Yy= (x-suckle m6 ni3 m/2 2m/3 5m/6 11 7m FIGURE 2. Find the area of the region shaded red.

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