Question

parametrization of the curve x=y^2+3

Answer 1

Find a parametrization of the curve x23+y23=1 and use it to compute the area of the interior.

I found the answer at the following link example #5.

http://www2.math.umd.edu/~jmr/241/lineint2.htm

u=x12 and y=y12 so they could get u2+v2=1, which is a nice trick. I can see how they parameterized that to u=cost, v=sint from t=0 to t=2π.

Answer 2

Then do you know the next step?

Answer 3

if not: Since I presume you already know cos2u+sin2u=1, set x23=cos2u (and similarly for y), and solve for x and y in those two equations. The curve you have, BTW, is called an astroid.

Answer 4

or in other words You want u=x13, v=y13