IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

sudesh

Sir,

pl. tell me general meaning of differential calculus & integration, so that a small 10th pass student can undertand. tell me in detail with example.

Prabhuling

concider a function y=f(x) let

y be the change in y with respect to change in

x in x.

y\

x is the average change in y with respect to x. the average rate

of change of y with respect to x is called .......................

krishna.gopal

Sudesh let me explain you with example. Suppose a car is moving at a constant speed. For such a car will have a changing position, but rate of change of position will be constant (which is speed). If this car is at delhi at 2:00 pm today and i want to find its position at 5pm we know that distance is speed*time so it will be 60*3=180km from delhi.

Whose speed is not constant but changes with time. Suppose it is 60km/hr as 2:00 pm and keeps on increasing at a rate of 10km/hr in every hour (ie. its speed is 70 km/hr at 3pm, 80 km/hr at 4 pm amd 90 km/hr at 5pm) then what will be its position at 5pm.

You can't answer this question directly using distance=speed*time (because now speed is not constant)

Now diffferential and integral calculus are mathematical tools which will help you to solve this problem (and even problems much complicated then this)

How calculus does this is somethihng which can't be explained is such a post so i am sorry for that. Pick up books of class 11th and you will know how calculus is used to solve such problems

sudesh

Sir

I am always confuse in the real meaning of function & what is domain & range pl. tell me with example the meaning of funtion in differential calculus.

krishna.gopal

HI sudesh, I am sorry but i don't think that i can help you about these topics in these posts. This is like teaching a chapter of maths, which is not possible here.

edison

Differentiation at a point is like
finding slope of the curve at that point = slope of tangent at that point

Integration means finding area between curve and given axis (it can be x or y or z even) between the given limits.

asvin_1989

Let there be a plane which is having a definite area....

Suppose you know area of a very small portion and if you want to find it for the whole plane...U shud use integration....integration is nothing but summasion.....

But if u know the area of the whole plane and want to find area of a small portion of the plane..u shud use differentiation.......

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