Let f(x) be a differential or derivable function on [a, b]. Then corresponding to each point c ∈ [a, b], we obtain a unique real number

equal to the derivative f`(c) of f(x) at x = x. This correspondence between the points in [a, b] and derivatives at these points defines a

new real valued function with domain [a, b] and the range a subset of R, set of real numbers, such that the image of x in [a, b] is the

value of the derivative of f at x i.e. f`(x) or Df(x). This function is called the derivative or differentiation of f(x) with respect to x or

simply differentiation of f(x) and is denoted by f`(x) or Df(x) or df(x)/dx

Thus, df(x)/dx = lim_h->0 {f(x + h) - f(x)}/h

or df(x)/dx = lim_h->0 {f(x - h) - f(x)}/(-h)

Let f(x) be a function. Then the collection of all its primitives is called the integral of f(x) and is denoted by ∫f(x) dx

Thus, d{Φ(x) + c}/dx = f(x) = ∫f(x) dx

=> ∫f(x) dx = Φ(x) + c

Again, you can watch videos of these chapters at this website (class 12 Maths):

http://cdn.examfear.com/free-video-lesson/all