MATH 222 Midterm: MATH 222 Binghamton Midterm08 Exam2

• School: Binghamton University
• Department: Mathematical Science
• Course: MATH 222
• Professor: All

Document Summary

Math 222 calculus 2 fall 2008 exam 2 solutions (1) (40 points, 8 points each) evaluate the following integrals. (a) z x cos(x) dx. Using integration by parts with u = x and dv = cos(x)dx, we have du = dx and v = sin(x), so. Z x cos(x) dx = x sin(x) z sin(x)dx = x sin(x) + cos(x) + c (b) z tan8(x) sec4(x) dx. Let u = tan(x) so du = sec2(x)dx, and sec2(x) = 1 + tan2(x) = 1 + u2, so the integral becomes. Z tan8(x) sec4(x) dx = z tan8(x) sec2(x) sec2(x) dx = z u8(1 + u2) du. = z (u8 + u10) du = u9. Use integration by parts twice, the rst time with u = e2x and dv = cos(x)dx, so that du = 2e2x and v = sin(x), giving. Z e2x cos(x)dx = e2x sin(x) 2z e2x sin(x) dx.