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)

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 ...

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

for your problem ...

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

$y = \pm x^3 + C$

$6 = \pm 1^3 + C$

$C = 5$ or $C = 7$

two possible functions ...

$y = x^3 + 5$

$y = 7 - x^3$

awesome, thanks!