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What is the physical and geometrical meaning of differentiation and integration? As we says, the darivative of sine is cosine, what is the physical and geometrical meaning of this and also pls explain its application also

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Rate of change and area
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Math Expert

It's a very nice question amol, well if we talk about differentiation, differentiation is just to find out the rate at which something is changing. Talking about the motion if you see something moving how can you describe it's velocity? You can say total distance covered divided by total time that ... read more
It's a very nice question amol, well if we talk about differentiation, differentiation is just to find out the rate at which something is changing. Talking about the motion if you see something moving how can you describe it's velocity? You can say total distance covered divided by total time that is right but that is average velocity. Now if ask you what it's velocity at the 3rd second of its motion then what will you say?Then you will use differentiation. You can find the velocity at single precise second of time. See how useful differentiation is? Talking about integration, if I ask u what is integration probably you will say it is the inverse of differentiation, yes it is right but what does that mean. It simply means summation, with the help of differentiation you are breaking the entire motion into small pieces of interwal of time and each piece of time represent it's own velocity that can be or not be same now if you add up these pieces u find the find the whole that is what integration actually does. Geometrically integration is used to find the area under the curve well that I can explain u with the help of diagram. I hope you get your answer. Good luck read less
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Integration area Differentiation slope
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Physical meaning of differentiation is that it represent rate of change of parameter. For example differential of velocity graph will indicate accelaration. Integration inficated area uder a curve. For example integral of a graph of force against distance will indicate work done.
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Derivative means that one of the function (objects) is derived(produced) when another object changes. Lets say for example a person changes his distance in a time t. When changes his distance from specific point each time he is at a new distance from tat specific point.. In other words we can say that... read more
Derivative means that one of the function (objects) is derived(produced) when another object changes. Lets say for example a person changes his distance in a time t. When changes his distance from specific point each time he is at a new distance from tat specific point.. In other words we can say that he is moving or he has speed. Mathematically Speed = Derivative of distance = Changes happening to speed in a particular time Integration is the reverse of Derivate . You know a person speed(Function). You now wanna calculate the distance he has moved. To find the distance he has moved you just have to integrate the function(speed) Or You know the area of a particular piece of tile in a wall. To find the total area of the wall using the area of tile you just need to integrate the area of tile. read less
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Mathematics Teacher

Differentiation means the mesurement of rate of change of one variable with respect to other. Suppose a car is moving, then the variables time and speed can be related by taking the derivative of one with respect to the other. Integration is all about finding the area under a curve of the given grap...
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Integration gives area under the curve ..
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Science Field

Integration mean to add the small parts and combine them together whereas differentiation mean dividing(a big unit) in smaller parts.By integrating we get the area enclosed in it where as in differentiation we get the slope of it.
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Tutor--Maths, Yoga

iffrntition,,is,,rat,of,hang,of,a,partiular,,funato/ativity.Whras,,intgration,is,th,,summation/multipliation,,of,,th,,2or,,mor,,funtion,,whih,,ar,,attah,,to,,it
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