Calculus II Sample Gateway Exams – Summer 2001

Calculus Review Practice Sets for IntegralsDirections: Simplify answers completely. Evaluate trig functions completely. Do not leave negative exponents in youranswers. No calculators. No notes.Practice Set A Problems Practice Set B Problems Practice Set C Problems1.2.3.4.∫⎛ 3 1 2⎞dy4x e dx 1.1.⎜ + +2 ⎟3∫⎝ x ⎠( 3y + 1) 32sec 4x 3 2.2dx∫ 1tan 4x62x− 3 dx3.2 2tdy3. ∫ 6sin dt1 23y44.2 2 33cos xsinxdx4. x sec ( x − 2)dx∫2. ( )∫∫xdx5. ∫ 2x − 4∫1 46. ( x − )7.8.9.∫∫0 54 2dx( + 2)( + 5)t t dtπ /405cos2x dx5.6.7.8.∫∫∫∫∫1/30⎛⎜⎝2sinπx dx4x⎞⎟⎠16 x − + π x − dx32sin 2xcos 26 2x − 4x 4 dx2x22x+ 3∫ 8xedxπ z−19. e dz∫ x x dx10.210 sin ( 1−)∫∫e4−1 x−1dxxdx∫∫∫∫41 2 x dxtan1/6−1/6 ⎛⎜⎝2π x dxcos π x dx6− π + xx3/25. ∫ cos( 2 )6.7.∫∫5t t dt2xe2xe − 4tanx sec2 2xdx⎞⎟dx⎠2 −1/2 3/28. ∫ ( − 2 )∫x x x dx12 −19. e dy∫0 6 y10. 4 2x−1dx

Calculus Review Practice Sets for Integrals – Answer KeyPractice Set A – Answers Practice Set B - Answers Practice Set C - Answers1.2.3.4.5.6.7.8.9.1− + + 1.3x4 2x ex C1− + C63 1( y + ) 21 ln tan 4 x + C2. 282.4t13. − 24cos + C 4 3.331 4. 1 tan ( x − 2 ) + Ccos4− x + C34.41 15.ln 2x 4 Cπ23/2 2166. 4x + + π ln x + C2x6.1 3 7 2t + t + 10t+C1 33 27. sin 2 x + C67.51 3 22 8.6 x + +xC8.22 32ex + + C1 π z 19. e− + C1 π29.cos 1 − x + C210. 410. ( )1.2831 tanπx − x + Cπ1π12161/2 6x − πx+ x + C1 sin 233/2− + 5. ( t )1 ln2xe 421 tan33+ C− + Cx + C2 45 95/2 9/2x − x + C33e −e4 2 −31 + C10. ( x ) 3/2