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peter_peter

Member

Registered: 2009-02-24

Posts: 3

I want to get the length of a parabola

Hey guys, I have forgot how to do integration can you do the following calculation for me?

parabola formula: y=0.048x2 + 0.24x
length between x=0 and x=-5

please show me the step clearly as I have forgot how to do integration, thanks!

LampShade

Member

Registered: 2009-02-22

Posts: 23

Re: I want to get the length of a parabola

We need to use the arc length formula.

Since

We find that

Hence

Here is where we stop, because the quadratic under the radical has no real roots.  Given this fact (and the appearance of decimals) we employ the use of computer software (in my case, the free program Graphmatica) to get

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peter_peter

Member

Registered: 2009-02-24

Posts: 3

Re: I want to get the length of a parabola

can you tell me the next step?

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: I want to get the length of a parabola

That integral 'does' have an analytic solution: Observe:

To make things simpler: replace the constants with a,b

now substitute

now substitute

substitute back one step

back another step:

In thise case:
a = 0.096
b = 0.24

Last edited by luca-deltodesco (2009-02-24 22:54:06)

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LampShade

Member

Registered: 2009-02-22

Posts: 23

Re: I want to get the length of a parabola

Well met

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--  Boozer