Month: June 2022

Integral calculus is used for solving the problems of the following types. a) the problem of finding a function if its derivative is given. b) the problem of finding the area bounded by the graph of a function under given conditions. Thus the Integral calculus is divided into two types. Definite Integrals (the value of… Continue reading Types of Integrals

We define integrals as the function of the area bounded by the curve y = f(x), a ≤ x ≤ b, the x-axis, and the ordinates x = a and x =b, where b>a. Let x be a given point in [a,b]. Then  b∫a f(x)dx ∫abf(x)dx represents the area function. This concept of area function leads… Continue reading Fundamental Theorems of Integral Calculus

F(x) is called an antiderivative or Newton-Leibnitz integral or primitive of a function f(x) on an interval I. F'(x) = f(x), for every value of x in I. Integral is the representation of the area of a region under a curve. We approximate the actual value of an integral by drawing rectangles. A definite integral of a… Continue reading Definition of Integral

Integrals are the values of the function found by the process of integration. The process of getting f(x) from f'(x) is called integration. Integrals assign numbers to functions in a way that describe displacement and motion problems, area and volume problems, and so on that arise by combining all the small data. Given the derivative f’ of the function… Continue reading What is Integral Calculus?

Integral calculus helps in finding the anti-derivatives of a function. These anti-derivatives are also called the integrals of the function. The process of finding the anti-derivative of a function is called integration. The inverse process of finding derivatives is finding the integrals. The integral of a function represents a family of curves. Finding both derivatives and integrals form… Continue reading Integral Calculus