Find the area between these curves

Question

Hi, I need help finding the area between these curves. I get the principal of finding the area between curves (sorta) but i am mostly stuck finding out how to find the limits of the definite integral that i will need to calculate. 

 

y=13x^2-x^3+x,

y=x^2+36x

 

Thank you, 

Kait

 

Answer 1

you have to set them equal to each other and find those points,  y₁=13x²-x³+x=x²₊₃₆=y₂

-x³+12x²-36. so there could be up to 3 separate points since it x³ . Then next step would be to factor this. Assuming you have three separate points the area would switch at the middle point. In this case there be one integral y₁-y₂ from x point 1 to x point 2, and then another one y₂-y₁ from x point 2 to x point 3. Good luck