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