Question

Graph the given curve and find the area of a bounded region.

x= 3y^2 - 9

Answer 1

$x=3y^2-9$

factoring;

$y=\sqrt{\frac{x+9}{3}}$

$y=(\frac{x+9}{3})^{\frac{1}{2}}$

to find the area we integrate the function with respect to x

$\int_{-9}^{\infin} (\frac{x+9}{3})^{\frac{1}{2}}dx$

the integral is divergent hence the area can not be found as it is unbounded.