Question

How would you find the area bounded between y^2 -x = 2 and x -y = 0

Answer 1

I don't know what should be my upper bound...

Answer 2

First thing you need is a diagram. The upper and lower bounds will come from the intersections of the curves.

Answer 3

Would it then be possible to find where those curves intersect and use those are your bounds?

Answer 4

Based of, say, a system instead of graphing?

Answer 5

Nevermind, I got it.

Answer 6

Any time you are asked to find area or volume in a calculus question, you should use a diagram.

Answer 7

\[y^2=x+2\]
It is a parabola with vertex at (-2,0)
x-y=0 is a straight line.
x=y
\[x^2-x-2=0\]
\[x^2-2x+x-2=0\]
\[x(x-2)+1(x-2)=0\]
\[(x+1)(x-2)=0,\]
x=-1,2
as x=y
point of intersections are (-1,-1) and (2,2)