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## Homework Statement

I'm trying to compute the circumference of a wing section. I have broken up the airfoil circumference into arc pieces and used cubic splines to come up with an equation for each piece.

For example, the arc nearest the leading edge of the wing is the function:

y = 0.0290X

^{^3}-0.3334x

^{^2}+1.8645x+1.4155

To find the length of this arc, I use the Arc Length Formula:

L = ∫

_{a}

^{b}√(1+[f'(x)])

^{^2}dx

The integration limits are: a = 0.75, b = 5

## Homework Equations

Alternate notation for the arc length formula gives the derivative as dy/dx:

L = ∫

_{a}

^{b}√(1+[dy/dx])

^{^2}dx

## The Attempt at a Solution

I started by getting the derivative of the function:

f'(x) = dy/dx = 3(0.0290X

^{^2})-2(0.3334x)+1.8645

I then substituted u for the derivative term:

u = 3(0.0290X

^{^2})-2(0.3334x)+1.8645

Here's where I get bogged down. How do I get du in terms of dx? I tried differentiating u but that gives negative numbers so something is wrong.

I'm wondering if I should try integrating in parts? Or maybe I should first try to factor that polynomial?

Sorry about the lack of math characters. I tried to use latex but it would not work in my browser.

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