Pages similar to: Area and definite integrals
- Basic integration formulas
Formulas for integration based on reversing formulas for differentiation. - The simplest integration substitutions
Reversing a simple chain rule application to compute integrals. - Integration substitutions
Reversing the chain rule to compute integrals. - Length of curves
An integral to find the length of a curve. - Numerical integration
Methods to approximate the value of definite integrals and estimate the error in the approximations. - Averages and weighted averages
Using integrals to calculate averages and weighted averages of a function. - Centers of mass (centroids)
An integral to find the length of a curve. - Volumes by cross sections
Calculating the volume of a solid by integrating the area of its cross sections. - Volume of surfaces of revolution
Calculating the volume of created by rotating a plane region around some axis. - Integration by parts
Using the product rule backwards to simplify integrals. - Partial fractions
Using algebra to simplify the integral of rational functions. - Trigonometric integrals
Using trigonometric identities to calculate integrals involving trigonometric functions. - Trigonometric substitution
Using trigonometric substitution to simplify integrals involving square roots. - Developing intuition about the indefinite integral
An intuitive exploration into the properties of the indefinite integral, illustrated by interactive graphics. - Calculating the area under a curve using Riemann sums
Approximating the area under the graph of a positive function as sum of the areas of rectangles. - Elementary integral problems
Sample problems illustrating the indefinite and definite integral. - Solutions to elementary integral problems
Solutions to sample problems illustrating the indefinite and definite integral. - Double integrals as area
Explanation of how double integrals could be used to represent area. - Area calculation for changing variables in double integrals
A derivation of how a mapping that changes variables in double integrals transforms area. - Integrating Taylor polynomials: first example
An example showing how to integrate a Taylor polynomial and interpret the result.
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