PHYSICS 15A Midterm: PHYS15A Harvard 03 Fall Midterm1
Document Summary
Math 104 final exam spring 2011: consider the region that lies to the right of the y-axis and is enclosed between the graphs of y = x2 and y = 2x x3. 0: a pyramid with a square base lies on the x, y-plane, with the vertices of its base at the points (1, 1), (1, 1), ( 1, 1), ( 1, 1). The height of the pyramid is 2, and the vertex of the pyramid lies directly over the origin of the x, y-plane. 0 x sin(2x) dx. (a) /4 (b) /3 (c) /2 (d) (e) 2 (f) 3 : evaluate z 1. 2 x(cid:1) dx. (c) 2/3 (d) 1/3 (e) 3/4 (f) 4/3 : suppose that f (x) is a function such that f (x) = cos(x3). The trapezoidal rule is then used to approximate the integral z 1. 0 f (x) dx, using ten subintervals of equal length. 1 (c) |e| 1/1200 (f) |e| 1. dx.
