Okay so notice how the length of the arc is
S (a=>b) [1+{f'(x)}^2]^(1/2)
Since we're concerned with the function y = x^2
f'(x) = 2x
[f'(x)]^2 = 4x^2
So the function we are concerned with for Simpsons rule will become
[1+4x^2]^(1/2).
Now Simpsons rule is
A = h / 3 [ y0 + 4y1 + 2y2 + 4y3 + ... yn ]
where h is the distance between the x values
Since it asks for 5 function values, we take the values of x as 0, 0.5, 1, 1.5 and 2
So we sub this into the equation, and h becomes 0.5
L = 0.5 / 3 [ {1+0}^(1/2) + 4{1+4(0.5)^2}^(1/2) + 2{1+4(1)^2}^(1/2) + 4{1+4(1.5)^2}^(1/2) + {2+0}^(1/2) ]
Put those into a calculator and you should get the correct answer.
)^2} dx)
is the lenth of the arc of curve y = f(x) between x = a and x = b. Usig Simpson' rule with five function values, estimate the length of the graph y =x^2 between x = 0 and x =2. Answer correcto two dp.
