MATH 101 Quiz #3 (v.A1)
Last Name:
Friday, February 12
First Name:
Grade:
Student-No:
Section:
Very short answer question
Z
1. 1 mark Evaluate
sin84 x cos3 x dx.
Answer:
Short answer questions—you must show your work
Z
2. 2 marks Evaluate
2x arctan(x) dx.
3. 2 marks Find the work (in joules) required to stretch a string 10 cm beyond equilibrium, if
its spring constant is k = 50 N/m. Simplify your answer completely.
Answer:
Long answer question—you must show your work
2
4. 5 marks The finite region between the curves y = cos(x) and y = x2 − π4 is rotated about
2
the line y = − π4 . Using vertical slices (disks and annuli), find the volume of the resulting
solid. A calculator-ready answer is acceptable. (Hint: to find where the curves intersect, look
at where they both vanish.)