MATH 148 Assignment #1
Due: Monday, January 17 1) For each of the following limits of Riemann Sums identify the corresponding integral. In each case, sketch the graph of the function over the region of integration and nd the limit (integral). a) lim ( i )
Integrals Involving Trig Functions
In this section we are going to look at quite a few integrals involving trig functions and some of
the techniques we can use to help us evaluate them. Let's start off with an integral that we should
already be able to do
MATH 148 Assignment #6
1) Solve the following dierential equations:
i) y 4 e2x + y = 0
ii) y = x 1 + xy y
iii) y 3x2 y = x2
iv) x2 y + 5xy + 3x5 = 0
x = 0 ,y(1) = 0
v) y + y = 0 (Solve rst for y ).
2) Asume that at time t = 0 a tank contains 10 kg of salt
Math 148 Assignment #3
1) a) Evaluate each of the following indenite integrals.
i)
x+3
x(x1)2
dx
ii)
x+3
x2 +4x+5
dx
b) Let R be the region bounded by the graphs of y = sin(x), y = x, x = 0
and x = .
2
i) Find the area of the region R.
ii) Find the volume
MATH 148 Assignment #2
Due: Friday, February 4
1) Evaluate each of the following indenite integrals.
1
x ln(x)
i)
dx
ii)
iv)
iii) xe3x dx
2
x3 ex dx
v)
vii)
tan(x) dx
sin3 (t) dt
vi) x arctan(x) dx
csc(x) dx
viii)
dx
1sin(x)
2) Evaluate each of the follow
MATH 148 Assignment #4
Due: Wednesday, March 23
1) Find the radius of convergence and the interval of convergence for the
following power series:
i)
n=1
iii)
nxn
ii)
n
(2x
4n
n=0
(n!)k n
v)
x
(kn)!
n=0
2) Let
nn xn
n=1
n
1)
iv)
n=1
(1)n
(2n1)!
x2n1
where
MATH 148
Assignment 2
Due: Friday, January 24
At the end of each question the page is left blank. It would be most helpful to the TAs if
you print this assignment and write your solutions in the blank spaces below each question. Some
questions may require
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MATH 148
Assignment 5
Due: MONDAY, February 24
At the end of each question the page is left blank. It would be most helpful to the TAs if
you print this assignment and write your solutions in the blank spaces below each question. Some
questions
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MATH 148
ID#
Assignment 9
Due: MONDAY, March 31
At the end of each question the page is left blank. It would be most helpful to the TAs if
you print this assignment and write your solutions in the blank spaces below each question. Some
questions may
Integrals Involving Roots
In this section we're going to look at an integration technique that can be useful for some
integrals with roots in them. We've already seen some integrals with roots in them. Some can be
done quickly with a simple Calculus I sub
Integration Techniques
Introduction
In this chapter we are going to be looking at various integration techniques. There are a fair
number of them and some will be easier than others. The point of the chapter is to teach you
these new techniques and so thi
As this last example has shown us, we will sometimes need more than one application of
integration by parts to completely evaluate an integral. This is something that will happen so
don't get excited about it when it does.
In this next example we need to
Trig Substitutions
As we have done in the last couple of sections, let's start off with a couple of integrals that we
should already be able to do with a standard substitution.
x 25x 75
2
1 25x2 4 32 c
4 dx
x 1 25x 2 4 c dx
25
25x2 4
Both of these used
Integration Strategy
We've now seen a fair number of different integration techniques and so we should probably
pause at this point and talk a little bit about a strategy to use for determining the correct technique
to use when faced with an integral.
The
Comparison Test for Improper Integrals
Now that we've seen how to actually compute improper integrals we need to address one more
topic about them. Often we aren't concerned with the actual value of these integrals. Instead we
might only be interested in
Improper Integrals
In this section we need to take a look at a couple of different kinds of integrals. Both of these are
examples of integrals that are called Improper Integrals.
Let's start with the first kind of improper integrals that we're going to ta
Approximating Definite Integrals
In this chapter we've spent quite a bit of time on computing the values of integrals. However, not
all integrals can be computed. A perfect example is the following definite integral.
0
2
ex dx
2
We now need to talk a litt
Partial Fractions
In this section we are going to take a look at integrals of rational expressions of polynomials and
once again let's start this section out with an integral that we can already do so we can contrast it
with the integrals that we'll be do
Name:
MATH 148
ID#
Assignment 7
Due: WEDNESDAY, March 12
At the end of each question the page is left blank. It would be most helpful to the TAs if
you print this assignment and write your solutions in the blank spaces below each question. Some
questions