APPM 1360 Midterm: appm1360spring2017exam1_sol
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Spring 2017: (28 pts) evaluate the following integrals. (a) z x + 5 x2 + 25 dx (b) z tan3 u sec u du (c) z ln t t2 dt. Z x + 5 x2 + 25 dx = z dx +z. | {z } u=x2+25 du=2x dx (b) (10 pts) (c) (8 pts) Z tan3 u sec u du = z tan2 u tan u sec u du = z (cid:0)sec2 u 1(cid:1) {z v=sec u v3 v + c = tan u sec u du dv. {z sec3 u sec u + c. | {z : (22 pts) for this problem let i = z /6 u=ln t,du=dt/t v= 1/t,dv=dt/t2. + c (a) approximate i using the trapezoidal approximation t3. Solution: (a) (4 pts) (b) (6 pts) (c) (8 pts) 2 f = cos2(3x), f = 6 cos(3x) sin(3x) = 3 sin(6x), f = 18 cos(6x) (cid:12)(cid:12)f (cid:12)(cid:12) = |18 cos(6x)| 18 k = 18.
