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The Most Important Derivatives and Antiderivatives to Know

The table below shows you how to differentiate and integrate 18 of the most common functions. As you can see, integration reverses differentiation, returning the function to its original state, up to a [more…]

The Sum Rule, the Constant Multiple Rule, and the Power Rule for Integration

When you perform integration, there are three important rules that you need to know: the Sum Rule, the Constant Multiple Rule, and the Power Rule.

The Sum Rule for Integration tells you that it’s okay to [more…]

How to Solve Compound Functions Where the Inner Function Is ax + b

Some integrals of compound functions f(g(x)) are easy to do quickly in Calculus. These include compound functions for which you know how to integrate the outer function [more…]

Solve Compound Functions Where the Inner Function Is ax

When figuring Calculus problems, some integrals of compound functions f (g(x)) are easy to do quickly. These include compound functions for which you know how to integrate the outer function [more…]

Integration by Parts with the DI-agonal Method

The DI-agonal method is basically integration by parts with a chart that helps you organize information. This method is especially useful when you need to integrate by parts more than once to solve a problem [more…]

How to Solve Integrals with Variable Substitution

In Calculus, you can use variable substitution to evaluate a complex integral. Variable substitution allows you to integrate when the Sum Rule, Constant Multiple Rule, and Power Rule don’t work. [more…]

How to Use Integration by Parts

When doing Calculus, the formula for integration by parts gives you the option to break down the product of two functions to its factors and integrate it in an altered form. To use integration by parts [more…]

Calculus II For Dummies Cheat Sheet

By its nature, Calculus can be intimidating. But you can take some of the fear of studying Calculus away by understanding its basic principles, such as derivatives and antiderivatives, integration, and [more…]

Understanding Infinite Series in Calculus

In calculus, an infinite series is "simply" the adding up of all the terms in an infinite sequence. Despite the fact that you add up an infinite number of terms, some of these series total up to an ordinary [more…]

Evaluating Limits in Calculus

The mathematics of limits underlies all of calculus. Limits sort of enable you to zoom in on the graph of a curve — further and further — until it becomes straight. Once it's straight, you can analyze [more…]

Calculus: How to Solve Differentiation Problems

In calculus, the way you solve a derivative problem depends on what form the problem takes. Common problem types include the chain rule; optimization; position, velocity, and acceleration; and related [more…]

Calculus: Techniques of Integration

You'll find that there are many ways to solve an integration problem in calculus. The following list contains some handy points to remember when using different integration techniques: [more…]

Solving Integration Problems in Calculus

Calculus riddle: What do the Mean Value Theorem, the Washer and Shell Methods, and the Arc Length and Surface of Revolution formulas have in common? They all involve integration. Integration is very fancy [more…]

Calculus Workbook For Dummies Cheat Sheet

To effectively work through calculus problems, you have to understand a number of topics: the process of evaluating limits, methods of solving various differentiation and integration problems, and the [more…]

Classifying Differential Equations by Order

The most common classification of differential equations is based on order. The order of a differential equation simply is the order of its highest derivative. You can have first-, second-, and higher-order [more…]

Distinguishing among Linear, Separable, and Exact Differential Equations

You can distinguish among linear, separable, and exact differential equations if you know what to look for. Keep in mind that you may need to reshuffle an equation to identify it. [more…]

Defining Homogeneous and Nonhomogeneous Differential Equations

In order to identify a nonhomogeneous differential equation, you first need to know what a homogeneous differential equation looks like. You also often need to solve one before you can solve the other. [more…]

Using the Method of Undetermined Coefficients

If you need to find particular solutions to nonhomogeneous differential equations, then you can start with the method of undetermined coefficients. Suppose you face the following nonhomogeneous differential [more…]

Differential Equations For Dummies Cheat Sheet

To confidently solve differential equations, you need to understand how the equations are classified by order, how to distinguish between linear, separable, and exact equations, and how to identify homogenous [more…]

How to Do an Area Approximation Using Sigma Notation

Sigma notation comes in handy when you’re approximating the area under a curve. For example, express an 8-right-rectangle approximation of the area under [more…]

How to Use Trig Substitution to Integrate radicals of the sine form

Before reading this article, you should check out the discussion of trig substitution in the companion article, “How to Use Trig Substitution to Integrate.” [more…]

How to Analyze Position, Velocity, and Acceleration with Differentiation

Every time you get in your car, you witness differentiation first hand. Your speed is the first derivative of your position. And when you step on the accelerator or the brake — accelerating or decelerating [more…]

How to Express Exponential Relationships with Logarithms

You may come across logarithms in your calculus work. A logarithm is just a different way of expressing an exponential relationship between numbers. For instance, [more…]

How to Simplify Roots

When you work with roots in an equation, you often need to simplify them. There are two methods: the quick, sort of intuitive method, and a slightly longer method. The quick method of simplification works [more…]

How to Factor Mathematical Expressions

You often need to factor expressions (break those expressions into their simpler components, or factors) for calculus. Factoring means “unmultiplying,” like rewriting 12 as [more…]

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