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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,..

Theorem 7: - Let f be real valued function in [a,b] such that, f is continuous in [a,b]. f is differentiable in (a,b..

Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b..

Let f be real valued function in [a,b] such that, 1. f is continuous in [a,b]. 2. f is differentiable in (a,b). ..

Let f (x) be a single valued continuous function defined in the interval [a,b] where b > 0 and let the interval [a,b] be divided into n equal parts each of length h, so that nh = b - a; then we define The method of evaluating by using the above definition is called integratio..

x = a is called a point of inflexion. Rolle's theorem: If a function f(x) is such that (i) f (x) is continuous on [a,b] (ii) f (x) is differentiable on (a,b) and (iii) f (a) = f (b) Geometrical interpretation of Rolle's theorem Let AB be the graph of y = f(x) such that A = (a , ..

The area bounded by the curve x = f(y), y - axis and the abscissas If f(x) is continuous in [a,b] and crosses the x-axis at x = c in (a, b) then the area bounded by the curve, x - axis and x = a and x = b is Area between y = f(x) and y = g(x..

If f(x) is a continuous function on the closed interval [a, b], and if Area function is defined ..

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..