Math 106: Review for Exam I
1. Find the following. [Substitution tip: usually let u= a function that’s “inside” another function,
especially if du (possibly oﬀ by a multiplying constant) is also present in the integrand.]
1 + x6dx
x√10 −x dx
2. Suppose f(x) is decreasing and concave up.
(a) Put the following quantities in ascending order.
(b) What can you say with certainty about where S200 would ﬁt into your list above?
3. Suppose f(t) is the rate of change (in animals per month) of a population P(t).
(a) What does Z12
f(t)dt represent in this problem?
(b) Find the best possible left, right, midpoint, trapezoidal, and Simpson’s approximations to Z12
given the data in the table below.
t4 6 8 10 12
f(t) 15 11 8 4 3
4. Find bounds for each of the following errors if I=Z7
ln x dx.
5. If I=Z7
ln x dx, how many subdivisions are required to obtain a trapezoidal sum approximation with
error of at most 1/1,000,000?