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.]

(a) Z4

1

e√x

√xdx

(b) Z2π

π

cos7(5x) sin(5x)dx

(c) Z7x2

1 + x6dx

(d) Z10

6

x√10 −x dx

2. Suppose f(x) is decreasing and concave up.

(a) Put the following quantities in ascending order.

L100,R100,T100,M100,Zb

a

f(x)dx

(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

4

f(t)dt represent in this problem?

(b) Find the best possible left, right, midpoint, trapezoidal, and Simpson’s approximations to Z12

4

f(t)dt

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

2

ln x dx.

(a) |I−L100|

(b) |I−T100|

(c) |I−M100|

5. If I=Z7

2

ln x dx, how many subdivisions are required to obtain a trapezoidal sum approximation with

error of at most 1/1,000,000?

##### Document information

Uploaded by:
seri_66

Views: 729

Downloads :
0

Address:
Mathematics

University:
Punjab Engineering College

Subject:
Calculus

Upload date:
16/03/2013