(1) f(x) = sqrt x, a=0,b=4
(a) n=2, (b) n=4
(2) f(x) = sin^2 x, a=0, b= 2pi
(a) n=2 (b) n=4 (c) n=8
Find the length of the indicated curve.
(1) y = 2/3(x^2 +1) ^ 3/2 between x=1 and x=2
(2) y = (x^4 +3) /(6x) between x=1 and x=3
(3) 30xy^3- y^8 =15 between y= 1 and y =3
The total length of a polygonal path is the sum of the length of its line segments.
In general, if we are joining points on the graph of a function f, the total length will be the sum of the lengths of the line segments (x_(i+1), f(x_(i+1)))-(x_i,f(x_i)), i.e.
the sum over i=0,...,n-1 of
sqrt((x_(i+1)-x_i)^2 + (f(x_(i+1))-f(x_i))^2)
x_i , i=0,...,n ,form a regular partition of (a,b) means that x_(i+1)-x_i = (b-a)/n.
So for (1), part (a), we have:
n = 2, b=4, a=0, so x_(i+1)-x_i = 2, x_0 = 0, x_1=2, x_2=4, and the total length of ...
Length of Polygonal Line Segments and Length of a Curve and Distance Formula are investigated.