I'm sorry, I cannot answer this question as it is not a topical webpage title.

[MillerGenuine]

Homework Statement

Find the length of the curve y=x^3 using P(1,1) as the starting point

Homework Equations

$$f(x) = \int_{a}^{x} {\sqrt 1 + {f'(t)}^2}$$

The Attempt at a Solution

So far all I've done is found my y' and plugged it in, giving me 1+9t^4 inside the square root...now from here I am not sure whate technique to use to do the integral.

 

[lanedance]

looks like a classic trig sub integral

 

[Char. Limit]

looks like a classic trig sub integral

If only. Checking Wolfram-Alpha, you'll require the Elliptic Integral of the First kind to solve this. A simple trig sub works with functions of the form sqrt(a^2 + (bx)^2), but not sqrt(a^4 + (bx)^4).

 

[lanedance]

fair bump, play on

 

[Mark44]

Homework Statement

Find the length of the curve y=x^3 using P(1,1) as the starting point

Homework Equations

$$f(x) = \int_{a}^{x} {\sqrt 1 + {f'(t)}^2}$$

The Attempt at a Solution

So far all I've done is found my y' and plugged it in, giving me 1+9t^4 inside the square root...now from here I am not sure whate technique to use to do the integral.

Is there an end point given? If so, you run into the problem pointed out by Char Limit. If not, are you just supposed to find an expression that represents the length from (1, 1) to an arbitrary point (x, x³)?

If it's the latter, here's a function that gives the length along the curve. Although difficult to integrate analytically, it can be approximated by a number of numerical integration techniques.
$$L(x) = \int_1^x \sqrt{1 + 9t^4}dt$$