Important notes: this is a sample exam. Disclaimer: i have tried to approximate the length, style and di culty level of the nal exam, but i cannot guarantee that you will nd both exams equally challenging. Also, you should not assume that the precise choice of subject matter in the sample exam is representative of the nal exam: the nal exam time is 2 hours. Try to simplify expressions e. g. , write 0 instead of ln(1). Question 1 (24 points) compute the following integrals: (a) (b) (c) (d) (e) (f) (x2 + sin(x)) dx. X (ey + e y) dy (note: the answer is a function of b) Question 2 (6 points) compute the arc length of the curve y = x3/6 + 1/(2x) from x = 2 to x = 3. Question 3 (36 points) compute the following integrals using integration by parts or (a) any other technique. 2 x(x 1)(x 2) dx.