MATH-0042 Midterm: w11exam1sol

• School: Tufts University
• Department: Mathematics
• Course: MATH-0042
• Professor: all

Document Summary

Solutions to math 42 first exam january 27, 2011: (12 points) evaluate each of the following integrals, showing all of your reasoning. (a) z e t3 ln t dt. 1 (6 points) consider u = ln t du = (1/t) dt. 1 z e t4 t3 ln t dt = (cid:20) t4. 0 dx (1 + x)5 (6 points) let u = x. 0 dx (1 + x)5 = z 1. Then dv = du; also, if u = 0, then v = 1, and if u = 1, then v = 2. This gives u = sec x du = sec x tan x dx. Z tan3 x sec x dx =z tan2 x tan x sec x dx. =z (sec2 x 1) tan x sec x dx u3. 3 sec x + c . (b) z x. 5 4x x2 dx (7 points) here we must complete the square, so we have.