MAT137Y1 Midterm: 2004 Test 3 solution

• School: UTSG
• Department: Mathematics
• Course: MAT137Y1
• Professor: N/ A

Document Summary

Mat 137y 2004-2005, solutions to term test 3: evaluate the following integrals. sec2 x tan x + 1 dx. = ln|u| = ln|tan x + 1| +c. dx = sec2 x tan x + 1. Z (10%) (i) (10%) (ii) (10%) (iii) (cid:19) d = 9. Substituting back, we see that sin2 = 2sin cos = 2 x. Z 2x2 x + 4 x(x2 + 4) dx. We decompose the rational function using partial fractions: Z 1 so a = 1, b = 1, and c = 1. Z 2x2 x + 4 x(x2 + 4) dx = = a(x2 + 4) + bx2 +cx = 2x2 x + 4 = . 2. (10%) (i) find the volume generated by rotating the region bounded by the curves y = ex, y = e x, x = 1 about the y-axis. Since the region is being rotated about the y-axis, we use shells.