00:01
In this question we have given a curve that is y is equal to under root of 2 minus x square, where 0 is less than or equals to x is less than or equals to 1.
00:18
And we have to find the length of a curve using an arc length formula.
00:25
So the arc length formula is length is equal to integration from a to b.
00:36
Under root of 1 plus d .y divided by d x whole square dx.
00:48
So first we will find the derivative of the function with respect to x, that is, consider y is equal to under root of 2 minus x squared.
01:00
So it implies y prime or you can say dy divided by d x is equals to minus 2x divided by and the root of 2 minus x square.
01:15
Multiply this with 2.
01:18
So it implies d .y divided by d x is equals to minus x divided by under root of 2 minus x square.
01:29
So, on squaring both sides will get it as dy divided by d x whole square is equals to x square divided by 2 minus x squared.
01:42
Now substitute this value in equation 1.
01:49
Let us name this as 1.
01:54
So from 1 we have l is equal to integration is from a to b.
02:03
Here the limit is from 0 to 1 under root of 1 plus d.
02:11
D .x squared, that is x squared divided by 2 minus x square.
02:18
So it implies l is equals to integration from 0 to 1 under root of 2 minus x squared plus x squared divided by 2 minus x squared multiplied it with d x.
02:33
So it implies l is equal to integration from 0 to 1 under root of 2 divided by 2 minus x squared dh.
02:44
So it implies l is equal to integration from 0 to 1 root 2 divided by under root of 2 minus x square d x.
02:56
Let u is equal to x divided by root 2...