IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

ultimator

We can find area under the curve for a function using integration.

But can one find, the length of a curve, given as a function of a variable like x ?
Is it possible ? If so, someone tell me, plz.

By a function, i m not meaning the obvious, like st.lines or a circle or stuff.

Was jus thinkin abt it. If u got any ideas, plz post it here.

ultimator

Come on some1 !!!!

ultimator

Hey u goiitians over thr ! Plz help me abt this !!!

kmmankad

But arent most graphs going infinitely long?

kmmankad

so,in a way we do know the length,its infinite!.... ;)

ultimator

But even integration is like tat.

I am asking length of a graph over values of x, from x1 to x2 n like tat.

Wat abt finite length of functiton ?

me_living4u

yes integratio can be used to find length..... in fact it is used also....

just that u hve to hve a graph following a definite function and u hve to know some properties of curve or some relation( even in some cases that is not required)

consider a circle for example.....

to find its perimetr.

let radius gven b R

and d theta be any angle

so the small portion by it is R d theta ( which can b considered to b a straight line)

integrating Rdtheta frm 0 - 2pie

we get the ans as 2 pie R

which is infact the perimetr.

this is a simple example........ wat i wanted to show is integration is simply addition of smaller units... we integrate to find areas we can integrate to find volume and even length.....

Cheers!!!!!

ultimator

Hey man , i m not meaning integrating n finding dimensions of geometric objects, like we usually do !!!

I am asking about finding the length of a curve plotted on a graph ! That's wat i meant by a function !!! For example , to find the length of the graph y = x square between -1 to 1 and things like that ! We can find area under the graph using integration. What can we do to find the length of that y = x squre graph in terms of units wrt to x ?

sarthak_jain

calculate the integral (root((dy/dx)^2+1))*dx cause u have to calculate root((x2-x1)^2+(y2-y1)^2)

rhd92781

consider a small length element of the curve f(x) as PQ = dl. let the slope of dl be tan

. let PA = dx

In the curve, cos? = dx/dl

Now, tan? = dy/dx at P

so cos? = 1/(^{[ ]}

(1+(dy/dx)²))

you have, dl = dx/cos?

or dl =

(1+(dy/dx)²) dx.

find dy/dx from the eqn of the curve in terms of x and integrate dl from x1 to x2.

for example in your curve, y=x², dy/dx = 2x.

so dl = ^{[ ]}

(1+4x²) dx

ultimator

That was an example, i gave. thanks for the effort, though.

What i mean is , is it possible to find for most functions ? I think a similar method wud work. Thanks !

rhd92781

i havn't gone thru many functions but it will work on most of the functions where dy/dx can be expressed in terms of x alone and integration of the last terms is possible.

so this method won't work for implicit functions

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