# How do you find the lengths of the curve #y=int (sqrtt+1)^-2# from #[0,x^2]# for the interval #0<=x<=1#?

##### 1 Answer

May 15, 2017

The arc length of the curve

#L=int_a^bsqrt(1+(dy/dx)^2)dx#

Here, to find

#y=int_0^(x^2)(sqrtt+1)^-2dt#

#dy/dx=(sqrt(x^2)+1)^-2d/dx(x^2)=(x+1)^-2(2x)#

#(dy/dx)^2=(4x^2)/(x+1)^4#

So the arc length is given by:

#L=int_0^1sqrt(1+(4x^2)/(x+1)^4)dx#

Putting this into a calculator or Wolfram Alpha:

#L=1.07943#