Exam #1 Solutions
1. (20 points) Evaluate the following integrals:
(a) (10 points) t2 +2tt+17 .
This is an irreducible quadratic; its denominator can thus be rephrased via completion
of the square as a sum of two squares, which under appropri
Exam #2 Solutions
1. (15 points) The region shown below is the area between the curves y = 3x and y = x2 . Find
the center of mass of this region.
We must calculate the area, x-moment, and y -moment to nd the center of mass.
Practice Exam #1
Note: in accordance with requests to limit the scope of the exam, this practice
exam does not, nor will the actual exam, cover sections 7.7 and 7.8. You will, however,
be expected to know these sections for Quiz #3 and Exam #2.
Practice Exam #2 solutions
1. (15 points) The region shown below is the area between the curves y =
Find the center of mass of this region.
x and y = 1 x2 .
We must calculate the area, x-moment, and y -moment to nd the center
Quiz #2 Solutions
1. (6 points) Evaluate
(4x + 2) sin(2x)dx via integration by parts.
Since this integral is a product of a polynomial and an integrable function, our parts
decomposition will choose u to be the polynomial, and v the trigonometr