We will also briefly look at how to modify the work for products of these trig functions for some quotients of trig functions. Trig Substitutions — In this section we will look at integrals both indefinite and definite that require the use of a substitutions involving trig functions and how they can be used to simplify certain integrals. Partial Fractions — In this section we will use partial fractions to rewrite integrands into a form that will allow us to do integrals involving some rational functions.
Integrals Involving Roots — In this section we will take a look at a substitution that can, on occasion, be used with integrals involving roots. In some cases, manipulation of the quadratic needs to be done before we can do the integral. We will see several cases where this is needed in this section. Integration Strategy — In this section we give a general set of guidelines for determining how to evaluate an integral. The guidelines give here involve a mix of both Calculus I and Calculus II techniques to be as general as possible.
Improper Integrals — In this section we will look at integrals with infinite intervals of integration and integrals with discontinuous integrands in this section. Collectively, they are called improper integrals and as we will see they may or may not have a finite i. Determining if they have finite values will, in fact, be one of the major topics of this section. Comparison Test for Improper Integrals — It will not always be possible to evaluate improper integrals and yet we still need to determine if they converge or diverge i.
So, in this section we will use the Comparison Test to determine if improper integrals converge or diverge. Approximating Definite Integrals — In this section we will look at several fairly simple methods of approximating the value of a definite integral. It is not possible to evaluate every definite integral i. These methods allow us to at least get an approximate value which may be enough in a lot of cases. Probability — Many quantities can be described with probability density functions.
For example, the length of time a person waits in line at a checkout counter or the life span of a light bulb. None of these quantities are fixed values and will depend on a variety of factors. In this section we will look at probability density functions and computing the mean think average wait in line or average life span of a light blub of a probability density function. Parametric Equations and Curves — In this section we will introduce parametric equations and parametric curves i.
We will graph several sets of parametric equations and discuss how to eliminate the parameter to get an algebraic equation which will often help with the graphing process. Arc Length with Parametric Equations — In this section we will discuss how to find the arc length of a parametric curve using only the parametric equations rather than eliminating the parameter and using standard Calculus techniques on the resulting algebraic equation.
We will derive formulas to convert between polar and Cartesian coordinate systems. We will also look at many of the standard polar graphs as well as circles and some equations of lines in terms of polar coordinates. We will also discuss using this derivative formula to find the tangent line for polar curves using only polar coordinates rather than converting to Cartesian coordinates and using standard Calculus techniques.
Area with Polar Coordinates — In this section we will discuss how to the area enclosed by a polar curve. We will also discuss finding the area between two polar curves. Arc Length with Polar Coordinates — In this section we will discuss how to find the arc length of a polar curve using only polar coordinates rather than converting to Cartesian coordinates and using standard Calculus techniques. Arc Length and Surface Area Revisited — In this section we will summarize all the arc length and surface area formulas we developed over the course of the last two chapters.
Sequences — In this section we define just what we mean by sequence in a math class and give the basic notation we will use with them. We will focus on the basic terminology, limits of sequences and convergence of sequences in this section.
More on Sequences — In this section we will continued examining sequences. We will determine if a sequence in an increasing sequence or a decreasing sequence and hence if it is a monotonic sequence. Series — The Basics — In this section we will formally define an infinite series. We will also give many of the basic facts, properties and ways we can use to manipulate a series.
We will also briefly discuss how to determine if an infinite series will converge or diverge a more in depth discussion of this topic will occur in the next section. We will illustrate how partial sums are used to determine if an infinite series converges or diverges. We will also give the Divergence Test for series in this section.
Special Series — In this section we will look at three series that either show up regularly or have some nice properties that we wish to discuss. Integral Test — In this section we will discuss using the Integral Test to determine if an infinite series converges or diverges.
The Integral Test can be used on a infinite series provided the terms of the series are positive and decreasing. A proof of the Integral Test is also given. In order to use either test the terms of the infinite series must be positive. Proofs for both tests are also given. Alternating Series Test — In this section we will discuss using the Alternating Series Test to determine if an infinite series converges or diverges.
The Alternating Series Test can be used only if the terms of the series alternate in sign. A proof of the Alternating Series Test is also given. Absolute Convergence — In this section we will have a brief discussion on absolute convergence and conditionally convergent and how they relate to convergence of infinite series. Ratio Test — In this section we will discuss using the Ratio Test to determine if an infinite series converges absolutely or diverges. The Ratio Test can be used on any series, but unfortunately will not always yield a conclusive answer as to whether a series will converge absolutely or diverge.
A proof of the Ratio Test is also given. Root Test — In this section we will discuss using the Root Test to determine if an infinite series converges absolutely or diverges. The Root Test can be used on any series, but unfortunately will not always yield a conclusive answer as to whether a series will converge absolutely or diverge. A proof of the Root Test is also given. Strategy for Series — In this section we give a general set of guidelines for determining which test to use in determining if an infinite series will converge or diverge.
A summary of all the various tests, as well as conditions that must be met to use them, we discussed in this chapter are also given in this section. Estimating the Value of a Series — In this section we will discuss how the Integral Test, Comparison Test, Alternating Series Test and the Ratio Test can, on occasion, be used to estimating the value of an infinite series. Power Series — In this section we will give the definition of the power series as well as the definition of the radius of convergence and interval of convergence for a power series.
We will also illustrate how the Ratio Test and Root Test can be used to determine the radius and interval of convergence for a power series. Instead, ask for a written lesson. First, you and your tutor agree on: Your tutor will return the completed work to you by the specified deadline.
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Get online tutoring and college homework help for Calculus. We have a full team of professional Calculus tutors ready to help you today! Calculus II. Here are my online notes for my Calculus II course that I teach here at Lamar University. Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn Calculus II or needing a refresher in some of the topics from the class.
Online Homework My Math Lab Login. Course ID: rimmer For instructions on how to create a login, follow the directions here. All homework will be due at midnight on the day listed. Online Hw # 1 - Due Sunday 1/ and 3D Coordinates and Introduction to Vectors Note this is actually broken into 2 links in My Math Lab. I need help with Calculus II, webAssign homework. The questions is basic and about anti-direvitives. Please contact me for more information.