PHYSICS 15A Midterm: PHYS15A Harvard 03 Fall Midterm1 Solutions
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0 (b) 1 cos(x)esin(x) dx. (c) e (d) e + 1 (e) e 1 (f) e2 e. 0 p1 x2 dx. (c) 14 ln 2 3 (d) 6 ln 2 + (e) e + 4 ln 2 (f) cos(4) cos(2) 2 y3 + y dy. (a) 2 ln(y3 + y) + c (d) + c (e) ln(2y2 + 1) + c (f) 2 ln |y| y + c: evaluate the improper integral z . 4 (e) (c) (b) (f) it is divergent. (a: the curve de ned by y = 1 + 2x, between x = 1 and x = 3, is rotated about x-axis. 1: consider the region in the rst quadrant that lies below the graph of y = sin(x2) + cos(x2), to the left of x = p /2. Let a be the area of this region. Then the x-coordinate of the center of mass of this region is (a)
