Comparison between Differentiation and Integration( i) Both differentiation and integration are linear operator on functions as
d / dx { af( x) ± bg( x)} = a d / dx { f( x) ± d / dx { g( x)} and ∫ [ a. f( x) ± b. g( x) dx = a ∫f( x) dx ± b ∫g( x) dx
( ii) All functions are not differentiable, similarly there are some function which are not integrable.
( iii) Integral of a function is always discussed in an interval but derivative of a function can be discussed in a interval as well as on a point.
( iv) Geometrically derivative of a function represents slope of the tangent to the graph of function at the point. On the other hand, integral of a function represents an infinite family of curves placed parallel to each other having parallel tangents at points of intersection of the curves with a line parallel to Y-axis.
Rules of Integration
Method of Substitution