what is proposition calculus?

The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverse operations: if a continuous function is first integrated and then differentiated, the original function is retrieve..

Let f(x) be a continuous function on the closed interval [a, b]. Let the area function A(x) be defined by th..

Let f(x) be a continuous function defined on an interval [a,b]. between the limits a and b. This statement is also known as 'fundamental theorem of calculus'. We call b, the upper limit of x and a, the lower limit. If in place of F(x) we take F(x)+c as the value of the integral, we have =..

Differential calculus can be considered as mathematics of motion, growth and change where there is a motion, growth, change. Whenever there is variable forces producing acceleration, differential calculus is the right mathematics to appl..

Introduction - The derivative, measures the rate at which the dependent variable changes with respect to the independent variable. It is one of the most important ideas in Calculus. The differentiation of functions are widely used in science, economics, medicine and computer scienc..

. Economists use differentiation to maximise profit with minimum cost. Differentiation is also used to study the behavior of machinery. What could be the shape of a least expensive machine, which can work effectively? Calculus enables to estimate the reduction in water levels as..

First Fundamental Theorem of Integral Calculus Let f(x) be a continuous function on the closed interval [a, b]. Let the area function A(x) be defined ..

From the above two theorem, we infer the following (Anti derivative of the function f(x) at b) - (Anti derivative of the function f(x) at a) (ii) The fundamental theorem of integral calculus shows a close relationship between differentiation and integration (iii) These theorems give an..

We have already defined, for a continuous function f(x) on a closed interval [a, b] as the area of the region bounded by the curve y = f(x), X-axis and x= a and x = b. In other words, area of the shaded region is a function of x. The function A(x) is shown in figure below. This area function A(x) i..

Integration by Partial Fractions - Before using this technique of integration, let us recall what we have learnt about partial fracti..