MATH 152 Midterm: MATH 152 TAMU 2009a Exam 1a Solutions
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0: d: fave = x sin(x2) dx. Using u- substitution, with u = x2, we obtain. 1: a: use integration by parts, with u = ln x and sin(u) du = . Then du = and v = dx x. 1 = 4 ln 2 : d: the total work is the work done to pull the rst. 10 feet of the rope to the top plus the work done to pull the remaining weight of rope up 10 feet. ) = 225 foot pounds: b: here, we will use the identity cos2 = Z 1 (1 + cos(4x)) dx sin(4x)(cid:19) + c: e: using the method of cylindrical shells, v = Z 2 washers, v = z 4: b: the curves y = x2 and y = 8 x2 intersect at the points (2, 4) and ( 2, 4). (y (8 x2 x2) dx = 1 (b3 b2) = b2 b.
