The length of a curve from x=1 to x=4 is given by
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)
The length of a curve from x=1 to x=4 is given by
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 ...
$\displaystyle S = \int_a^b \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx$
for your problem ...
$\displaystyle \frac{dy}{dx} = \pm 3x^2$
$\displaystyle y = \pm x^3 + C$
$\displaystyle 6 = \pm 1^3 + C$
$\displaystyle C = 5$ or $\displaystyle C = 7$
two possible functions ...
$\displaystyle y = x^3 + 5$
$\displaystyle y = 7 - x^3$