ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 14 Dec 2014 20:33:04 +0100Maximize the integral of an implicit relation with two parametershttps://ask.sagemath.org/question/25270/maximize-the-integral-of-an-implicit-relation-with-two-parameters/ Suppose we have an equation:
$${(r\cos{(t)}+u})^{2}+{(-(r\sin{(t)}+v)^3+1)}^{\frac{2}{3}}=1$$
Where $x=r\cos{t}$ and $y=r\sin{t}$
The graph of this implicit relation has two regions, where one part is above the x-axis, and the other part is below the x-axis.
Suppose we're are trying to find the area of the relation above the x-axis, between the x-values ${0}\le{x}\le{2\pi}$. How can one solve for the values of u and v that can give the highest area for this equation that's is above the x-axis, so that u and v as point (u,v) is still inside the implicit relation $$(1-x^2)^3=(1-y^3)$$.
Note: The blue stripes should stop at $2\pi$, and if the equation has regions that are "UNDEFINED", try to ignore it.
**I MADE EDITS!**
Krishnan ArbujaSun, 14 Dec 2014 20:33:04 +0100https://ask.sagemath.org/question/25270/