I am going to delete this question in 30 minutes since this edit as I have got link to another similar question.Thanks for letting me know.

This question may seem to be off-topic, So before flagging or reporting as off topic, feel free to comment and I will delete this question.

I have recently studied high school calculus and I am still wondering that how are integrals and derivatives related to each other?

Is this just a coincidence?

Or there is a logic that I am still not aware of.

Out of my curiosity I asked this question to my teacher but I didn't get any satisfactory answer.

And one more question,

How definite integrals calculate area of the given function.I asked this too, then my teacher replied that when we integrate $y(x).dx$ ; $dx$ is a small strip of width $dx$, parallel to $y$-axis and $y$ is it's height, so together multiplied it gives area in that rectangular region and the integral sums it up.

But then I found a question on this website asking : Is $\frac {dy}{dx}$ not a fraction? and it turned out that it isn't.Therefore we can't consider $dx$ as width, after all, it's a operator.

So what is going on?

This question may seem to be off-topic, So before flagging or reporting as off topic, feel free to comment and I will delete this question.

I have recently studied high school calculus and I am still wondering that how are integrals and derivatives related to each other?

Is this just a coincidence?

Or there is a logic that I am still not aware of.

Out of my curiosity I asked this question to my teacher but I didn't get any satisfactory answer.

And one more question,

How definite integrals calculate area of the given function.I asked this too, then my teacher replied that when we integrate $y(x).dx$ ; $dx$ is a small strip of width $dx$, parallel to $y$-axis and $y$ is it's height, so together multiplied it gives area in that rectangular region and the integral sums it up.

But then I found a question on this website asking : Is $\frac {dy}{dx}$ not a fraction? and it turned out that it isn't.Therefore we can't consider $dx$ as width, after all, it's a operator.

So what is going on?

This question may seem to be off-topic, So before flagging or reporting as off topic, feel free to comment and I will delete this question.

I have recently studied high school calculus and I am still wondering that how are integrals and derivatives related to each other?

Is this just a coincidence?

Or there is a logic that I am still not aware of.

Out of my curiosity I asked this question to my teacher but I didn't get any satisfactory answer.

And one more question,

How definite integrals calculate area of the given function.I asked this too, then my teacher replied that when we integrate $y(x).dx$ ; $dx$ is a small strip of width $dx$, parallel to $y$-axis and $y$ is it's height, so together multiplied it gives area in that rectangular region and the integral sums it up.

But then I found a question on this website asking : Is $\frac {dy}{dx}$ not a fraction? and it turned out that it isn't.Therefore we can't consider $dx$ as width, after all, it's a operator.

So what is going on?

I am going to delete this question in 30 minutes since this edit as I have got link to another similar question.Thanks for letting me know.

This question may seem to be off-topic, So before flagging or reporting as off topic, feel free to comment and I will delete this question.

I have recently studied high school calculus and I am still wondering that how are integrals and derivatives related to each other?

Is this just a coincidence?

Or there is a logic that I am still not aware of.

Out of my curiosity I asked this question to my teacher but I didn't get any satisfactory answer.

And one more question,

How definite integrals calculate area of the given function.I asked this too, then my teacher replied that when we integrate $y(x).dx$ ; $dx$ is a small strip of width $dx$, parallel to $y$-axis and $y$ is it's height, so together multiplied it gives area in that rectangular region and the integral sums it up.

But then I found a question on this website asking : Is $\frac {dy}{dx}$ not a fraction? and it turned out that it isn't.Therefore we can't consider $dx$ as width, after all, it's a operator.

So what is going on?