Pages similar to: Solutions to elementary integral problems
- Elementary integral problems
Sample problems illustrating the indefinite and definite integral. - Area and definite integrals
Integrating to find the area under a curve or the area between two curves. - Developing intuition about the indefinite integral
An intuitive exploration into the properties of the indefinite integral, illustrated by interactive graphics. - 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. - Using the Forward Euler algorithm to solve pure-time differential equations
By pretending that the slope of a function is constant over small intervals, we following tangent lines to estimate the solution to pure-time differential equations. - 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. - Introduction to double integrals
The definition of a double integral is motivated through a hair density example. - Double integrals as iterated integrals
A description of how to convert double integrals into two single integrals.