The Simpsons (1 Viewer)

[fullonoob]

L = 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.
thx

 

[Tofuu]

 

[ilikebeeef]

I like watching The Simpsons.

 

[fullonoob]

thats trap rule + its f'(X)

 

[fullonoob]

hmm lost still...

 

[life92]

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.

 

[fullonoob]

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.

YAYAYAY thanks you did minor error though (in bold)
damn i subbed in y values instead of x....silly me

 

[life92]

Oh my bad.
Should be 1+4(2)^2 instead ..
XD

 

[Tofuu]

thats trap rule + its f'(X)

ahh, oops, my bad