Formulas You Need to Know for Calculus
When 'studying calculus, you should have a good understanding of the following tables of formulas so you can efficiently and correctly solve calculus problems: [more…]
Calculus For Dummies Cheat Sheet
Calculus requires knowledge of other math disciplines. To make studying and working out problems in calculus easier, make sure you know basic formulas for geometry, trigonometry, integral calculus, and [more…]
How to Find a Normal Line Perpendicular to a Tangent Line
A line normal to a curve at a given point is the line perpendicular to the line that’s tangent at that same point. Find the points of perpendicularity for all normal lines to the parabola [more…]
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 Approximate Area with Midpoint Sums
A good way to approximate areas with rectangles is to make each rectangle cross the curve at the midpoint of that rectangle's top side. A midpoint sum is a much better estimate of area than either a left [more…]
How to Approximate Area with the Trapezoid Rule
With the trapezoid rule, instead of approximating area by using rectangles (for example, as you do with the left and right sum methods), you approximate area with — can you guess? — trapezoids. [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 Complicated Shape with the Meat-Slicer Method
You can use the meat-slicer method to determine the total volume of a complicated shape. In geometry, you learned how to figure the volumes of simple solids like boxes, cylinders, and spheres. Integration [more…]
How to Find the Volume of a Circular Shape with the Stack-of-Pancakes 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. The stack-of-pancakes technique works [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 Find the Volume of a Cylindrical Shape with the Nested-Russian-Dolls 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. You can cut up a solid into thin concentric [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…]
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…]
How to Vertically Transform a Function
To transform a function vertically, you add a number to or subtract a number from the entire function, or multiply it by a number. To do something to an entire function, say [more…]
How to Solve Limits by Conjugate Multiplication
To solve certain limit problems, you’ll need the conjugate multiplication technique. When substitution doesn’t work in the original function — usually because of a hole in the function — you can use conjugate [more…]
How to Solve Limits at Infinity by Using Horizontal Asymptotes
Horizontal asymptotes and limits at infinity always go hand in hand. You can’t have one without the other. If you’ve got a rational function like [more…]
The Basic Differentiation Rules
Some differentiation rules are a snap to remember and use. These include the constant rule, power rule, constant multiple rule, sum rule, and difference rule. [more…]
How to Work with Lines in Calculus
A line is the simplest function that you can graph on the coordinate plane. (Lines are important in calculus because when you zoom in far enough on a curve, it looks and behaves like a line.) This figure [more…]
How to Recognize Inverse Functions
You can tell that two functions are inverse functions when each one undoes what the other does. When you graph inverse functions, each is a mirror image of the other. Here are some examples of inverse [more…]
