MAT 127 Midterm: S06mt1sol

• School: University of Maine
• Department: Mathematics and Statistics
• Course: MAT 127
• Professor: All

Document Summary

Midterm i solutions: (20 pts) compute the following integrals. (a) z xex2 dx. Then du = 2x dx, and the above is. Let u = x and dv = exdx, so that du = dx and v = ex. 0 exdx: (20 pts) compute the following integrals. (a) z cos3(x) sin4(x) dx = z cos2(x) sin4(x) cos(x)dx = z (1 sin2(x)) sin4(x) cos(x)dx. Let u = sin(x), so du = cos(x)dx. = z (1 u2)u4du = z (u4 u6)du = u5. + c. (b) z 2x + 1 x2 + 4 dx = z. This one is just like 2b on the sample midterm. The second integral equals (1/2) arctan(x/2): make the substitution u = x2 + 4 in the rst integral. = z 1 u du + (1/2) arctan(x/2) + c = ln|x2 + 4| + (1/2) arctan(x/2) + c: (10 pts) (a) give the form of the partial fractions decomposition of.