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### How to Approximate Area with Left Sums

You can approximate the area under a curve by using left sums. For example, say you want the exact area under a curve between two points, 0 and 3. The shaded area on the left graph in the below figure [more…]

### How to Approximate Area with Right Sums

You can approximate the area under a curve by using right sums. This method works just like the left sum method except that each rectangle is drawn so that its right upper corner touches the curve instead [more…]

### How to Do Simple Integration by Parts

Integrating by parts is the integration version of the product rule for differentiation. The basic idea of integration by parts is to transform an integral you [more…]

### How to Change Unacceptable Forms before Using L'Hôpital’s Rule

You can use L'Hôpital’s rule to find a limit for which direct substitution doesn't work. If substitution produces one of the unacceptable forms, ± ∞ · 0 or ∞ – ∞, you first have to tweak the problem to [more…]

### How to Use Tangent Substitution to Integrate

With the trigonometric substitution method, you can do integrals containing radicals of the following forms: [more…]

### How to Use Sine Substitution to Integrate

With the trigonometric substitution method, you can do integrals containing radicals of certain forms because they match up with trigonometric functions. A sine can take the place of a radical in a particular [more…]

### How to Find the Average Value with the Mean Value Theorem for Integrals

You can find the average value of a function over a closed interval by using the mean value theorem for integrals. The best way to understand the mean value theorem for integrals is with a diagram — look [more…]

### How to Find the Volume of a Shape Using the Washer Method

Geometry tells you how to figure the volumes of simple solids. Integration enables you to calculate the volumes of an endless variety of much more complicated shapes. If you have a round shape with a hole [more…]

### How to Analyze Arc Length

You can add up minute lengths along a curve, an *arc,* to get the whole length. When you analyze arc length, you divide a length of curve into small sections, figure the length of each section, and then [more…]

### Statistics Terms to Know when Using Excel 2007 Data Analysis Tools

With the data analysis tools available in Excel 2007, you can create spreadsheets that show the details of any statistic you can create a formula to find — and you can find any number. It helps to know [more…]

### Factoring Special Problems

Binomials, their powers, and their products with selected trinomials occur frequently in algebraic processes. By using the patterns shown here, you save time and reduce the opportunity for errors. [more…]

### Formulas for Common Geometric Shapes

Depending on the algebra problem, you'll need to know some geometry. The following represents some of the most common shapes in geometry and their formulas for perimeter, area, volume, surface areas, and [more…]

### Order of Operations in Algebra

When creating simpler and more useful expressions, you want to be careful not to change the original value. By applying the order of operations, you maintain that value. [more…]

### Rules of Exponents

Exponents are shorthand for repeated multiplication. The rules for performing operations involving exponents allow you to change multiplication and division expressions with the same base to something [more…]

### Selected Math Formulas Step by Step

Algebraic formulas make life (and algebra) simpler. You save time by not having to perform more complicated tasks. When using the formulas, use the appropriate rules for simplifying algebraic expressions [more…]

### Algebra Workbook For Dummies Cheat Sheet

Formulas, patterns, and procedures used for simplifying expressions and solving equations are basic to algebra. Use the equations, shortcuts, and formulas you find for quick reference. This Cheat Sheet [more…]

### Simple Steps for Solving Word Problems

Word problems aren’t just on school tests. You solve word problems every day in your work or even while you’re just out and about. Don’t worry — these steps make solving word problems easier than you think [more…]

### Calculating a Standard 15-Percent Tip

Calculating a 15-percent tip in your head may seem tricky, but here’s a, well, tip for those situations when you need to calculate that standard tip amount. And it works 100 percent of the time. In order [more…]

### Counting Change for Customers the Old-Fashioned Way

Although many cashiers simply dump all your change in your hand at once, counting change the old-fashioned way ensures that customers get the proper amount. Here’s an easy way to make a customer’s change [more…]

### Matching American and Metric Units of Measurement

If you’ve ever had to match American and metric measurement units, you know direct comparisons of these unit systems can be tricky. If you need to know the metric equivalent of an inch, for example, or [more…]

### Technical Math For Dummies Cheat Sheet

Grasping some technical math basics can simplify everyday situations faced by many professionals and even non-professionals, including having to solve word problems, calculate tips, make change, or match [more…]

### Using Calculators on the SAT

When taking the SAT, you're allowed to use a calculator. Calculators can save a lot of time on the SAT if you save them for when you can't quickly and easily do a calculation in your head. The more complicated [more…]

### Topics Covered in the Math Sections of the SAT

You have a much better chance of getting a good SAT math score if you know what to expect. Focusing your study time on what will be included in the math sections of the SAT [more…]

### How to Interpret Function Graphs

You’re going to see dozens and dozens of functions in your study of calculus, and the graphs of those functions can visually express such things as inflation, population growth, and radioactive decay. [more…]

### How to Horizontally Transform a Function

You can transform any function into a related function by shifting it horizontally or vertically, flipping it over (reflecting it) horizontally or vertically, or stretching or shrinking it horizontally [more…]