Math 30: Final Exam
Fall Semester 2006
Instructions. Read each problem carefully and follow all of its instructions. For each
of the problems below, write a clear and concise solution in your blue book. For any
short answer questions, write clearly your answer and any additional explanation that is
needed.
1. (5 points) Find Zxsin(2x)dx.
2. (5 points) Find Z2
−2f(x)dx, where f(x) = (1x≤1,
x x >1.
3. (5 points) Find Z1
√1−4x2dx.
4. (5 points) Find the arc length of the curve given parametrically as x=2 sin(t)and
y=2 cos(t)for 0 ≤t≤2π.
5. (5 points) Consider the region bounded by the curves y=xand y=x2. Find the
volume of the solid generated by rotating that region about the y-axis.
CONTINUED ON THE BACK
