PHYSICS 15A Midterm: PHYS15A Harvard 04 Fall Midterm1 Solutions

• School: Harvard University
• Department: Physics
• Course: PHYSICS 15A
• Professor: All

Document Summary

4: evaluate z 1 (a) 2 , evaluate z e (a) e e 2, evaluate z 1. 0 (a) 0 (b) 1 ln x x2 dx. (b) 1 dx. 2 e (c) ln e2 e4 (d) 1 . 3 e (e) ln 2 1 (f) 2e. 4 x2 (c) 1 + (d) /6 (e) /2 (f) 2 (d) /8 (e) e/9 (f) cos 2. 4 2x: evaluate z 2 (a) /4 1/2, evaluate the improper integral z 2 (x + 2)(x2 + 4) (b) 1 (c) 32/51. 3 /2 (b) 1/ ln 2 (c) 1. 442 dx. 3 (x 1) (d) 1 e: find the arclength of the part of the curve x = and (2 6, 2). (a) 10/3 (d) 14/3 (b) 7/3 (c) 2 (e) 1 (f) 5/3 (e) 2. 3 (y2 + 2) (f) the integral is divergent. 2 exp1 + e2x dx (b) z 1 (e) z 1.