Chapter Overview
The chapter 'Integrals' introduces the concept of integration, the reverse process of differentiation. It includes indefinite and definite integrals, standard results, integration methods (substitution, partial fractions, and integration by parts), properties of definite integrals, and the application of integrals in calculating area under curves. This chapter forms the foundation for calculus and is essential for advanced studies in mathematics, physics, and engineering.
Important Keywords
- Integral: The reverse process of differentiation; a fundamental operation in calculus.
- Indefinite Integral: An integral without limits, representing a family of functions and includes a constant of integration (C).
- Definite Integral: An integral with limits of integration; gives a specific numerical value.
- Integrand: The function to be integrated.
- Limits of Integration: The upper and lower bounds in a definite integral.
- Integration by Substitution: Method involving a change of variable.
- Integration by Parts: Method for integrating the product of two functions.
- Integration by Partial Fractions: Decomposing rational expressions into simpler fractions before integration.
Detailed Notes
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