MATH 101 Quiz #3 (v.M1) Last Name: Friday, February 12 First Name: Grade: Student-No: Section: Very short answer question Z 1. 1 mark Evaluate tan62 x sec4 x dx. Answer: Short answer questions—you must show your work Z 2. 2 marks Evaluate log x dx. x3 3. 2 marks A 10-meter-long cable of mass 7 kg is used to lift a bucket off the ground. How much work is needed to raise the entire cable to height 10 m? Ignore the weight of the bucket and its contents. Use g = 9.8 m/s2 for the acceleration due to gravity. A calculator-ready answer is acceptable. Long answer question—you must show your work 4. 5 marks √Let a > 0 be a constant. Let R be the finite region bounded by the graph of 2 y = 1 + xex , the line y = 1, and the line x = a. Using vertical slices, find the volume generated when R is rotated about the line y = 1.