What is the difference between derivatives and integration?

Answer 1

There is a nice history about this topic

Isaac Newton and G Leibnitz discovered these concepts almost at the same time (12 years of diference in XVII century) Derivative is looking for instant variation of a function. and means the slope of a tangent line of the graph of the function in every point

Integral is looking for the area under a graph

Barrow's rule proves that this pair of problems are inverse one of each other

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Answer 2

They are opposites of each other...

Say I have a position #x# of a particle, then we define the velocity of the particle to be #(dx)/(dt)#, where #t# represents the time in seconds.
Now, let's say I have the velocity of the particle as #v#, then the position of the particle would be #intv \ dt#.

Let's try another example if that wasn't clear enough.

The derivative of #x^2# is #(x^2)'=2x#.
Now, the integral of #2x# would be #int2x \ dx=x^2+C#, where #C# is constant.

I hope you can figure it out from here!

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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