Background:
I was taught basic formulas of differentiation and integration when I started learning physics. However, it wasn't taught through intuitions and concepts. It was like : " Hey these are some common formulas. Learn them. We'll use them in physics for derivations."
As said, it was used for deriving things. I would like to give a specific example which was very commonly done while learning physics to illustrate my question :
" Consider a rod of length d$x$. The electric field due to this is d$E$. To get net field due to rod, we will add all field elements due to individual d$x$."
The electric field here was just an example. This method is very common like calculating moment of inertia($I$), distance travelled $(S)$, magnetic field per biot-savart law(d$B$), etc.
However, now after almost an year after that, I learnt that the integral of a function is the area under the curve of that function.(Assuming function as always positive like physical quantities are usually positive.)
Hence, I posed this problem. Why does adding elemental values of a function to get net(or say collective) value is same as calculating area of that function under the given variable?
Can you make it easier for me to understand that how the mathematical perspective (the area of the function $y=1$ with respect to variable electric field) is related to physics perspective ( The field of a system due to addition of field of it's small components)
Moreover, I have also got to know that things like elemental quantities like electric field due to small component d$E$ is meaningless. Because d$E$ is not a number/value.
