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- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/01%3A_IntegrationThis page discusses iceboats, used in winter sports on lakes, which glide on runners and can achieve high speeds. It also covers the concept of integration, detailing its use for calculating distance ...This page discusses iceboats, used in winter sports on lakes, which glide on runners and can achieve high speeds. It also covers the concept of integration, detailing its use for calculating distance from velocity, its theoretical principles like area approximation and the Fundamental Theorem of Calculus, and various integration techniques with specific applications, including net change and functions such as exponential, logarithmic, and inverse trigonometric.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.05%3A_Other_Strategies_for_IntegrationIn addition to the techniques of integration we have already seen, several other tools are widely available to assist with the process of integration. Among these tools are integration tables, which a...In addition to the techniques of integration we have already seen, several other tools are widely available to assist with the process of integration. Among these tools are integration tables, which are readily available in many books, including the appendices to this one. Also widely available are computer algebra systems (CAS), which are found on calculators and in many campus computer labs, and are free online.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.07%3A_Improper_IntegralsIn this section, we define integrals over an infinite interval as well as integrals of functions containing a discontinuity on the interval. Integrals of these types are called improper integrals. We ...In this section, we define integrals over an infinite interval as well as integrals of functions containing a discontinuity on the interval. Integrals of these types are called improper integrals. We examine several techniques for evaluating improper integrals, all of which involve taking limits.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.08%3A_SubstitutionThis page covers methods for simplifying non-separable differential equations through substitution, particularly Bernoulli equations, highlighting the significance of making effective substitutions to...This page covers methods for simplifying non-separable differential equations through substitution, particularly Bernoulli equations, highlighting the significance of making effective substitutions to achieve linear forms for easier solutions. It provides examples demonstrating the use of the substitution v=yx for homogeneous equations, illustrating the process of transforming complex equations into simpler, separable ones.
