MATH 125 Midterm: MATH 125 UW 125 Fall 12 Sol2

• School: UW
• Department: Mathematics
• Course: MATH 125
• Professor: All

Document Summary

Math 125, sections f and g, autumn 2012, solutions to midterm ii: evaluate the following integrals. (a) z x ln(x + 4) dx. Integration by parts: u = ln(4 + x) dv = xdx du = 4 + x dx now use long division and integrate. Z x ln(x + 4) dx = x2 ln(x + 4) + 2x 8 ln|x + 4| + c (b) z 1. Inverse trig substitution: 2x = sec and 2dx = sec tan d . 0 sec tan sec3 tan d = 4z. 3 cos2 d using the double angle formula. 1 + cos 2 d = 2 + sin 2 (cid:12)(cid:12)(cid:12) 1 (a) determine if it converges or diverges using the comparison theorem. 12 x2 + (p = 2 and p = 3) 3 1 (b) now evaluate it to see if it diverges or converges. To evaluate the improper integral we use limits.