Pages similar to: Calculating the area under a curve using Riemann sums
- Area and definite integrals
Integrating to find the area under a curve or the area between two curves. - 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. - 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. - Using Green's theorem to find area
A trick to use Green's theorem to calculate the area of a region - Area calculation for changing variables in double integrals
A derivation of how a mapping that changes variables in double integrals transforms area. - Surface area of parametrized surfaces
An introduction to surface area of parametrized surfaces, illustrated by interactive graphics. - Calculation of the surface area of a parametrized surface
A calculation deriving the expression for the surface area of a parametrized surface. - Parametrized surface area example
An example of calculating the surface area of a parametrized surface. - Length, area, and volume factors
A summary of the expansion factors that arise from mappings in integrals of multivariable calculus. - Determinants and linear transformations
A description of how a determinant describes the geometric properties of a linear transformation. - 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.