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- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/01%3A_Integration/1.04%3A_Integration_Formulas_and_the_Net_Change_TheoremThe net change theorem states that when a quantity changes, the final value equals the initial value plus the integral of the rate of change. Net change can be a positive number, a negative number, or...The net change theorem states that when a quantity changes, the final value equals the initial value plus the integral of the rate of change. Net change can be a positive number, a negative number, or zero. The area under an even function over a symmetric interval can be calculated by doubling the area over the positive x-axis. For an odd function, the integral over a symmetric interval equals zero, because half the area is negative.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/01%3A_Integration/1.07%3A_Integrals_Resulting_in_Inverse_Trigonometric_Functions/1.7E%3A_Exercises_for_Section_1.7This page presents exercises on evaluating integrals, emphasizing inverse trigonometric functions and substitutions. It includes definite integrals with solutions, techniques for finding antiderivativ...This page presents exercises on evaluating integrals, emphasizing inverse trigonometric functions and substitutions. It includes definite integrals with solutions, techniques for finding antiderivatives, and addresses undefined integrals. The text also covers integral calculations involving trigonometric and exponential functions, detailing methods to determine constants for definite integrals.
- 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/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.03%3A_Integrals_as_SolutionsThis page discusses solving first-order ordinary differential equations (ODEs) using integration, detailing the standard form and methods for general solutions. It differentiates between indefinite an...This page discusses solving first-order ordinary differential equations (ODEs) using integration, detailing the standard form and methods for general solutions. It differentiates between indefinite and definite integrals, supplemented by examples illustrating ODE applications in mechanics. Additionally, it provides two calculus problems involving a car's speed and acceleration, showcasing how to calculate distance through integration over specified time intervals.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_IntegrationIt is no surprise, then, that techniques for finding antiderivatives (or indefinite integrals) are important to know for everyone who uses them. We have already discussed some basic integration formul...It is no surprise, then, that techniques for finding antiderivatives (or indefinite integrals) are important to know for everyone who uses them. We have already discussed some basic integration formulas and the method of integration by substitution. In this chapter, we study some additional techniques, including some ways of approximating definite integrals when normal techniques do not work.
