APPM 1345 Midterm: appm134spring2015exam2_sol
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Spring 2015: (40 points) evaluate the following. dx (a) z x + 3 x dxz sec x. 3x (b) d tan x pt2 + t + 3 dt (c) z t t 17 dt (d) z 6/ (e) suppose h is an even function. 2 h(x) dx = 7, what is the value of (a) 3 x1/2 + x1/3 + c (b) use the fundamental theorem of calculus and the chain rule. d dxz sec x tan x pt2 + t + 3 dt = d. 0 pt2 + t + 3 dt z tan x dx(cid:18)z sec x. Z t t 17 dt =z (u + 17) u du =z (cid:16)u3/2 + 17u1/2(cid:17) du = u5/2 + 5 (t 17)5/2 + (t 17)3/2 + c. 3 (d) first let u = 1/x, du = 1/x2. The u limits are then /4 to /6. /4 sin2 u cos u du =z /4.
