MATH 1120H Final: MATH1120H-Final-Solutions
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Mathematics 1120h calculus ii: integrals and series. 19:00-22:00 on monday, 30 july, in cgs 105. Instructions: do parts a, b, and c, and, if you wish, part d. show all your work and justify all your answers. Aids: any calculator; (all sides of) one aid sheet; one (1) brain (no neuron limit). Do all four (4) of 1 4: evaluate any four (4) of the integrals a f. [20 = 4 5 each: z /4, z u + 1 u3 u, z 0, z (cid:0)1 + w2(cid:1)1/2 dx b. Z 1 dw e. z x2 + 2x + 2 ve v dv. Note that x2 + 2x + 2 = x2 + 2x + 1 + 1 = (x + 1)2 + 1. We will use this fact and the substitution u = x + 1, so du = dx and x 1. 1 (x + 1)2 + 1 dx =z 1 dx =z 0.
