Answer:
Dimensionally speaking multiplication corresponds to integration, and differentiation corresponds to division
How does multiplication correspond to integration? i mean how come foot-pound & pound-foot is defined from the definition & meaning of multiplication then as what is the difference between foot-pound & pound-foot too from the definition of units?
Aside from the fact that if differentiation corresponds to division, its inverse must correspond to the inverse of division, consider it this way.
An integral from a to b is the area under the curve - which is the limit as you take many rectangles with a width (b-a)/n, and n is the number of rectangles, and a height f(x).
The area of a given rectangle is f(x_o)*(b-a)/n, which is multiplication. The integral is the sum of many of these rectangles, and therefore also has units the same as the quantities multiplied.