- #1
soofjan
- 18
- 0
Homework Statement
Find the area, whose edge is given by the following curve:
sqrt(|x|) + sqrt(|y|) = 1
Also, draw the area.
Guidance: try x = r*cos(t)^k, y = r*sin(t)^k for a fitting k.
Homework Equations
The Attempt at a Solution
I tried:
x = r*cos(t)^4, y = r*sin(t)^4
From the curve equation, I get that: sqrt(r)=1. So:
0 [tex]\leq[/tex] r [tex]\leq[/tex] 1
0 [tex]\leq[/tex] t [tex]\leq[/tex] 2*pi
|J| = 4r*|sin(t)^3*cos(t)^3|.
Since I have an absolute value as the integrand, I calculate the integral of t from 0 to pi/2, and multiply the result by 4. The final answer is 2/3.
I believe that my transformation is wrong, because when I try to draw it via Wolfram, it gives me a circle, but it is supposed to look like an astroid.
Any help would be appreciated. Thanks!