# Basic Difference Between Two Ideas

Discussion in 'Differentiation and Integration' started by nycmathguy, Jul 13, 2021.

1. ### nycmathguy

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What is the basic difference between differentiation and integration?

nycmathguy, Jul 13, 2021
2. ### MathLover1

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Differentiation is used to calculate the gradient of a curve. It is used to find out the instant rates of change from one point to another.
Integration is used to calculate the area under or between the curves.
Integration is the reversed process of differentiation.

MathLover1, Jul 14, 2021
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3. ### nycmathguy

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I look forward to calculus.

nycmathguy, Jul 14, 2021
4. ### HallsofIvy

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Differentiation and integration were initially treated as completely different operations. Part of the reason that Newton and Leibniz are considered the founders of the Calculus is that they recognized that these are the inverse to each other.

HallsofIvy, Nov 8, 2021
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5. ### nycmathguy

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Newton and Leibniz hated each other, right?

nycmathguy, Nov 8, 2021
6. ### HallsofIvy

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I've never heard that. After their deaths, the English pretty much attributed the invention of the Calculus entirely to Newton while the French attributed it entirely to Leibniz, starting a "rivalry" that they never participated in. Speaking of Newton, Leibniz said "Taking mathematics from the beginning of the world to the time when Newton lived, what he has done is much the better part." That doesn't sound like Leibniz hated Newton!

HallsofIvy, Nov 9, 2021
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7. ### nycmathguy

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I simply stated what someone once said about the competition between the two math guys. Never did I read anything about the life of either of the men.

nycmathguy, Nov 9, 2021
8. ### HallsofIvy

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Perhaps you should not state "what someone once said" as if you knew it were a fact!

HallsofIvy, Nov 21, 2021

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