The problem I'm attempting is: Sketch the curves $\ x = y^2 − 4y$ and $\ x = 2y − y^2$, find their points of intersection, and find the area enclosed by the curves.
I'm confused as to how to graph the curves because they're given as x=... I tried to solve for y to get the function in terms of x but I couldn't isolate y on it's own.
I can see by using a graphing calculator that the curves are sideways parabolas (hyperbolas?) and I can set the equations equal to each other to find the intersection points $(-3,3)$, $(0,0)$
I would then find the area by integrating $\ \int_{0}^{3} {[(2y-y^2) - (y^2-4y)]} dy$ which I calculated to be 9.
Can someone please explain how I go about graphing a function that is given in terms of $y$ instead of $x$. I tried to look it up but I couldn't find anything.
Thanks