Sketching Functions 
Sketch the region enclosed by $x+y^2=30$ and $x+y=0$. Decide whether to integrate with respect to $x$ or $y$. Then find the area of the region. 

How do I start off sketching? Very first step?
I'm in Calc 2 and it's sad that I don't know what to do but I am trying to learn.

Can you sketch $y=30-x^2$? This is fairly standard highschool stuff. Once you do that, flip it over the line $y=x$ to interchange the $x$ and $y$ coordinates, to get $x=30-y^2$. That’s your first graph. The other one is easier, it’s $y=-x$ (you can also think of it as $x=-y$), still standard highschool stuff. With your two pictures, you are ready to go. You’ll need to know the points of intersection, those are where $x=30-y^2$ and $x=-y$, in other words where $30-y^2=-y$. Solve for $y$ by putting them all on one side of the equals sign, $0$ on the other side, and then factoring your quadratic in $y$.
