Okay so I'm not just looking for answer but I really need help conceptualizing which curve when using more than 2 belongs as the "top curve".
The problem I'm working with right now is
$y=x^2$, $y=2x-1$ ,$y=0$
I've graphed them out and found the points of intersection to be $(0,0), (1/2,0),$ and $(1,1).$
now when I take the integral I understand that the answer will be two integrals summed together. The first limit will be from $\int^.5_0$ (fractions don't appear to play well with the knowledge I have of formatting) and the second will be $\int^1_.5$.
What I don't under stand is why the solution isn't
$\int^.5_0 2x-1 -( 0)dx + \int^1_.5 x^2 -(2x -1)dx$
which once solved would give you $23/24$
Checking my work with Wolfram Alpha says it should be
$\int^.5_0 0 - (x^2)dx + \int^1_.5 2x -1 - (x^2)dx$
which equals $-1/12$
but $x^2$ is the upper boundary throughout the entire graph. So I don't understand why Wolfram Alpha subtracts it twice or why it is included in the integral of $\int^.5_0$ because that intersection point is of $y=0$ and $y=2x-0$ I'm going to start finding the area of shells and washers and discs so I really want to understand this.