MATH 101 Quiz #3 (v.T2)
Last Name:
Thursday, February 11
First Name:
Grade:
Student-No:
Section:
Very short answer question
1. 1 mark Find the average value of f (x) = sin(5x) + 1 over the interval −π/2 ≤ x ≤ π/2. Your
answer must be fully simplified.
Answer:
Short answer questions—you must show your work
2. 2 marks A 9-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 9 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.
3. 2 marks Evaluate the following integral, leaving your answer in calculator-ready form.
Z
1
4
√
3 x log x dx.
Long answer question—you must show your work
√
√
4. 5 marks Let R be the region between the curves T (x) = xe3x and B(x) = x(1 + 2x)
on the interval 0 ≤ x ≤ 3. (It is true that T (x) ≥ B(x) for all 0 ≤ x ≤ 3.) Compute the
volume of the solid formed by rotating R about the x-axis. You may leave your answer in
calculator-ready form.