Anyone understand Calculus 3 (ch. 13) Arc Length in Space?

Question

I am taking an online math class and there was a question I got wrong but I believe I was correct on it. Open the link to see the question. Its on Calculus 3.

 

http://s8.postimg.org/93wm0sxpx/untled.png

 

If anyone is familar with this math question, could you please check if the website's answer was correct or was my answer correct?

Answer 1

arc Length = L = integral of sqr(1+ f'(x))dx evaluated from x =a to x= b

hif f(x) = x^2 the arc length from x= 0 to x=1 is the length of the graph from (0,0) to (1,1) which is curved and more than the straight line connecting them, more than sqr2 = 1.414

f'(x) = 2x

sqr(1-2x) is integrated with respect to x, then evaluated from 0 to 1

use integral tables, and either trigonometric substitution or hyperbolic substitution

integral of sqr(1-2x) dx = x(1-4x^2)/2 + arcsin(2x))/4

or (2sqr5 + ln(2 +sqr5))/4

when evaluated from 0 to 1

'= about 4.7894