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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..

Introduction to Differentiation - After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable.After having studied functions, limits and continuity in the previous chapter,..

Introduction - Let us began this chapter with the following statement: Often a physician may want to test how small changes in dosage can affect the body's response to a particular drug. An economist may want to study how investment changes with variation in interest rates. How the velocity of a he..

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..

Let y = f(x) be a smooth curve and P(x,y) be a point on the curve. Equation of the tangent at (x 1 , y 1 ) in the curve y = f (x) is y - y 1 Equation of the normal at (x 1 , y 1 ) in the curve y = f (x) is If m = 0 the tangent at (x 1 , y 1 ) is parallel to x-axis. Angle of..