Integration is just formulas of area of the graph for different curves. which people found by different methods curated under one name
We represent in this way: Y dx (graph of y & x) The formula of y must be dependent on x we put the relation in place of y and then we put the formula from integration’s library of curves and their areas
we can also exchange y and dx in terms of some other variable. dx will still be dx and y will still be y just in terms of a different variable
Like the integration of J dA to find the total charge in an area (j is charge distribution, j = q/A )
if j was a constant we could have just done j * A
But j is variable, j = Jnot * x
so we will take some small area * J (note: j * area was giving total charge in case of constant J)
Don’t let that make you think some how following the steps will add these small rectangles giving you the complete area under the curve (it is just used for explaining what integration does). It is represented in this way so that if x is also changing with respect to another variable it can be put instead of dA, dA in its dA form is completely ignored. In the final answer dA is removed
This is a graph of J as y, area as x and area of graph is the total charge
we can put dA as 2Pi*x and J as Jnot*x
note: integration of constant is contant * x
so integration of 1 is x
