/sci/ - Science & Math

[Anonymous No.2295335]

Hey sci, i need your help in an mathematical problem.
How can i calculate the lenght of the following algebraic curve in parametric equation?
x = 5t^4
y = 4t^5
0<=t<=1

[Anonymous No.2295360]

Given a generic curve <span class="math">\gamma(t)[/spoiler], with <span class="math">t \in [a,b][/spoiler] its length is given by

<div class="math">L = \int_a^b \left\| \frac{d\gamma}{dt} \right\| dt</div>

[Anonymous No.2295361]

<div class="math"> \int_a^b \sqrt{\bigg(\frac{dx}{dt}\bigg)^2+\bigg(\frac{dy}{dt}\bigg)^2}\,dt,</div>