MAT137Y1 Lecture : MAT 137Y 2007-08Winter Session, Self Generated Solutions to Problem Set 10.pdf
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Mat 137y 2007-08 winter session, solutions to problem set 10. 1 (she 6. 1: see the gure below left. The area of the region (ax = ay) is. 0 (2 y) dy: see the gure above right. The curves intersect when x + x3 = 2x6 = 2x6 x3 x = 0 = x(2x5 x2 1) = 0. Hence the points of intersection are (0,0) and (1,1). 3 sinx = sin2x = sinx = 2sinxcosx = x = 0, (cid:90) /3 (cid:20) Cos2x (cid:90) /2 (cid:20) sin2x sinx dx + = sinc = (cid:90) b (a) the area of the region from x = 1 to x = b is a = A(b) = 1, so as b , the area is nite. (b) since lim b . 2 (she 6. 2: the sketch of the region is given above left. (cid:2)(2 x)2 x4(cid:3) dx = (cid:20) (cid:90) 2. 5: the sketch of the region is given above right.
