MATH 101 Quiz #3 (v.M3) Last Name: Friday, February 12 First Name: Grade: Student-No: Section: Very short answer question Z 1. 1 mark Evaluate sec4 x tan46 x dx. Answer: Short answer questions—you must show your work Z 2. 2 marks Evaluate log x dx. x4 3. 2 marks A 5-meter-long cable of mass 8 kg is used to lift a bucket off the ground. How much work is needed to raise the entire cable to height 5 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 √ xb2 > 0 be a constant. Let R be the finite region bounded by the graph of y = −1 + xe , the line y = −1, and the line x = b. Using vertical slices, find the volume generated when R is rotated about the line y = −1.