## List of integrals of exponential functions

Note that some sections will have more problems than others and some will have more or less of a variety of problems. Most sections should have a range of difficulty levels in the problems although this will vary from section to section. Here is a list of all the sections for which practice problems have been written as well as a brief description of the material covered in the notes for that particular section. Integration by Parts — In this section we will be looking at Integration by Parts. We also give a derivation of the integration by parts formula. Integrals Involving Trig Functions — In this section we look at integrals that involve trig functions. In particular we concentrate integrating products of sines and cosines as well as products of secants and tangents. 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. Practice Quick Nav Download. You appear to be on a device with a "narrow" screen width i. Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width.

## Integral Formulas ## 6.8: Exponential Growth and Decay Here are a set of practice problems for the Applications of Integrals chapter of the Calculus I notes. Note that some sections will have more problems than others and some will have more or less of a variety of problems. Most sections should have a range of difficulty levels in the problems although this will vary from section to section. Here is a list of all the sections for which practice problems have been written as well as a brief description of the material covered in the notes for that particular section. Average Function Value — In this section we will look at using definite integrals to determine the average value of a function on an interval. We will also give the Mean Value Theorem for Integrals. We will determine the area of the region bounded by two curves. More Volume Problems — In the previous two sections we looked at solids that could be found by treating them as a solid of revolution. Not all solids can be thought of as solids of revolution and, in fact, not all solids of revolution can be easily dealt with using the methods from the previous two sections. Work — In this section we will look at is determining the amount of work required to move an object subject to a force over a given distance. Practice Quick Nav Download. You appear to be on a device with a "narrow" screen width i. Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. 