Differential Calculus and Integral Calculus Is differential calculus a prerequisite for integral calculus? Because almost always you see that differential is taught before integral. Does that have a specific reason? Would it be recommended to start with integral calculus? Or is it an absolute non-go
The wonderful Analysis by Its History by Hairer and Wanner presents a first year calculus course by introducing the different topics in chronological order of their discovery. Of course this means that a fair bit of integration comes before some differentiation. The historical route is a great way to motivate the different definitions etc, and to see how mathematical knowledge is constructed/discovered. And its also a great way to learn calculus - it's not in the least pedagogically awful!
In integration, we make use of differentiation, particularly when we are making substitutions.

While learning differentiation, we need not have the knowledge of differentiation.

Further, integration is called the reverse process of differentiation.

Hence, we have to learn differentiation before integration.
Differentiation helps one to understand a whole with micro-level approach to understand whole from inside out in the entire domain of a function, and it's mechanics is pathological analysis in nature. Integration is understanding of coverage of a given function in the Cartesian domain, in any co-ordinate definition system. Approach is reverse of approach to human understanding. Differential calculus is a child while integral calculus is grand parent. One first learns the evolution of child and then understands the old person. Differential coefficient, being tangent of inclination of function, is akin to psychology and behavioral pattern of the child; while integral calculus approach is the tendency of old generation to define it's domain boundaries.

It is, hence, essential to start understanding the child in all its ramifications before undertaking to understand of its higher generation in terms of latter's domain perceptions.