I've attached the problem I'm working on. I didn't think doing these types of problems when there were only two curves was too bad but where would I even begin now that there's three? How do I know what to subtract from what to subtract from what? I've sketched it and I can figure it out from that but...then what becomes the bounds of the integral. I'm so confused
Ok I found it to be 1/2 between 4x^2 and-5x+6, 1 between x^2 and -5x+6 and the obvious 0. Now I'll have two integrals, one from 0 to 1/2 and the other from 1/2 to 1, but what values do I subtract from what? Just whatever values were used to find those intersection points? Like between 4x^2 and -5x+6 I'd use 4x^2 as the upper and -5x+6 as the lower with the integral with bounds 1/2 to 1? Which ones would I use from 0 to 1/2? I'll be doing this twice and just adding them?
Edit: I thought of a better way to word what I'm asking. I understand that I'll end up breaking it into two subintervals and adding them, but I don't understand what function would be associated with each curve...and how to find out this.
4x^2=-5x+6, how would I find this intersecting point? Because it could simplify out to 4x^2+5x=6 but I can't think of any number that would satisfy that? And then same with -5x+6=x^2, it doesn't simplify out evenly other than using 1, but what would the other value be?