Question

Find the area of the region that is enclosed between (y = 6x^{2}-x^{3}+x) and (y =x^{2}+5x)

Answer 1

do we know where they intersect yet?

Answer 2

I see that they intersect at 0 and (1,3)

Answer 3

Sorry, more like (1,5)

Answer 4

there are 3 points of intersection tha ti see

Answer 5

6x^2-x^3+x =x^2+5x; x=0 is obvious so

-x^2+6x+1 =x+5

0 = x^2 -5x+4

0 = (x-4)(x-1) , x=1 and x=4 are the other intersections

Answer 6

so we need to split out integral into 2 intevals and add the results

0 to 1 and 1 to 4

Answer 7

you have any thoughts on what to integrate?

Answer 8

I'm guessing one integral will have upper and lower limits of those two intersections, whilst integrating the equations they ask of us?

Answer 9

seems fair lets clarify a bit