MATH 101 Quiz #3 (v.T1)
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(3x) 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 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.
3. 2 marks Evaluate the following integral, leaving your answer in calculator-ready form.
Z
1
4
log x
dx.
x3/2
Long answer question—you must show your work
√
√
4. 5 marks Let R be the region between the curves T (x) = xe2x and B(x) = x(1 + x) 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.