# Equation for a Curve

• May 4th 2010, 02:19 PM
BeiW
Equation for a Curve
The length of a curve from x=1 to x=4 is given by http://www4a.wolframalpha.com/Calcul...=27&w=404&h=79
If the curve contains the point (1,6), what's the equation of the curve?

(Sorry, ignore the second part of that picture...it came with the plain integral part because I copied from Wolfram)
• May 4th 2010, 02:28 PM
skeeter
Quote:

Originally Posted by BeiW
The length of a curve from x=1 to x=4 is given by http://www4a.wolframalpha.com/Calcul...=27&w=404&h=79
If the curve contains the point (1,6), what's the equation of the curve?

(Sorry, ignore the second part of that picture...it came with the plain integral part because I copied from Wolfram)

arc length ...

$\displaystyle S = \int_a^b \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx$

$\displaystyle \frac{dy}{dx} = \pm 3x^2$

$\displaystyle y = \pm x^3 + C$

$\displaystyle 6 = \pm 1^3 + C$

$\displaystyle C = 5$ or $\displaystyle C = 7$

two possible functions ...

$\displaystyle y = x^3 + 5$

$\displaystyle y = 7 - x^3$
• May 4th 2010, 02:36 PM
BeiW
awesome, thanks!