MATH 145
WINTER 2008
SAMPLE EXAM II
This is intended to give you an idea of the length and difficulty of the second midterm exam. This
is not an exhaustive review. You will be expected to understand all concepts covered in class and
on homework.
1. Compute the integral.
(a) Z1
0
√1−x dx
(b) Ze
1
(1 + ln x)2
xdx
(c) Zcos x
√sin xdx
(d) Zx−2
x2(x−1) dx
(e) Z∞
0
1
(2x+ 1)2dx
(f) Z1
0
1
4
√xdx
(g) Z2
0
1
x4dx
2. The total weight of a bacteria colony changes at a rate of
w0(t) = (8t+ 1)2/3grams per hour.
(a) Find the change in the weight of the colony from t= 0 to t= 3.25 hours.
(b) If the colony weighs 29 grams at t= 2, how much does it weigh at t= 10?
3. The graph below shows the functions f(x) = x4
−8x3+ 18x2and g(x) = x+ 28. Compute
the area of the shaded region.
4. Find the average value of the function f(x) = xsin 1
5xon the interval [0,5π].
