MATH-0042 Final: w13finalsol
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Solutions to math 42 final exam march 18, 2013: (12 points) evaluate each of the following, or explain why its value does not exist; show all reasoning. (a) z 2. 0 (6 points) the integral is improper, because the integrand has a discontinuity at 0. 1 x3 dx t 0+z 2 t 0+ (cid:18) t 0+(cid:18) . Thus, the integral diverges (i. e. , its value does not exist). (b) z ex dx e2x + 1. Then we have du = exdx, and hence ex e2x + 1. 1 u2 + 1 arctan u|t (arctan t arctan 1) Set up two di erent integrals representing the volume of s1. In each case, cite the method used and justify with a sketch, but don"t evaluate either integral. (8 points) the region r is the area between the two parabolas, as in the gure below. 2 x2 1 = y = 1 x2.
