Explains integration of functions and their applications.
Introduce some simple rules for finding the integration of polynomial, trigonometric and logarithm functions.
Apply Rules of Definite Integrals.
9.1 Introduction
We have learned how to use the derivative of a function to solve a variety of real-life problems. But in a lot of other cases, we must recover a function from its known derivative, or from its known rate of change. In broader terms, we aim to identify a function F whose derivative is f. An antiderivative of f is a function F if one such function exists.
The core concept of differential calculus is the derivative. Derivatives are mostly used to solve graph-related problems and determine the slope of a line. Problems relation to the Area of the region bounded by the graph of the functions can be solved by finding antiderivatives, and the process of finding antiderivatives is known as Integral calculus.
Integral calculus originated from the attempts to solve two problems: finding the area bounded by a function’s graph under specific conditions, and finding a function whenever its derivative is known. These two issues result in the two types of integrals, definite and indefinite integrals, that together make up the Integral Calculus.
Integration of a function is the inverse process of differentiation. If F(x) is the ...
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