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

Question

phantomcrow · Answer

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

agent0smith · Answer

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

phantomcrow · Answer

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

phantomcrow · Answer

Based of, say, a system instead of graphing?

phantomcrow · Answer

Nevermind, I got it.

agent0smith · Answer

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

sshayer · Answer

$$y^2=x+2$$
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)

sshayer · Answer

|dw:1477699357405:dw|