PHYSICS 15A Midterm: PHYS15A Harvard 04 Fall Midterm2 Solutions
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There are twenty multiple choice questions on this examination. Show your work in the space provided, and then carefully transfer your answers to this sheet. No cal- culators, books, or notes may be used except for one two-sided 8. 5 x11 sheet of notes. /100: find the area of the surface generated by revolving the curve y = x3. 3 , 0 x 1 about the x-axis. (a) 1 (e) 4 2 . 12(cid:0)2 2 1(cid:1: find the area of the region bounded by y = 2 (c) 3 x and y = x + 3. (d) 6 (a) 0 (e) 3 (h) 3. 3 ln 2 (g) 6 ln 4. 6 ln 2: find the volume of the solid obtained by revolving the region bounded by the x-axis, the curve y = ln x, and the line x = e about the y-axis. (a) (f) . 2 (cid:0)e2 + 1(cid:1) (h) (c) (cid:0)e2 + 4(cid:1)
