Read all of the following information before starting the exam: complete each problem. Show all of your work clearly and in order and justify your answers, as partial credit will be given when appropriate and there may be no credit given for problems without supporting work. Circle or otherwise indicate your nal answers your nal answers. All answers should be completely simpli ed, unless otherwise stated. Evaluate the following inde nite integrals (i) r 5x3 + 6x2 2x + 1 x dx = 4 x4 + 2x3 x2 + ln|x| + c (ii) r. Z x sin xdx = sin(x) x cos(x) + c. Evaluate the following de nite integrals (i) r /2. 2t sin tdt = 2z t (cos t) dt = 2t cos t + 2z cos t = = ( 2t cos t + 2 sin t)| /2. /6 cos 2x 1 cos 2x + 1 dx = z 2 sin2 x.
