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

Question

amistre64 · Answer

do we know where they intersect yet?

anonymous · Answer

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

anonymous · Answer

Sorry, more like (1,5)

amistre64 · Answer

there are 3 points of intersection tha ti see

amistre64 · Answer

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

amistre64 · Answer

so we need to split out integral into 2 intevals and add the results

0 to 1   and   1 to 4

amistre64 · Answer

you have any thoughts on what to integrate?

anonymous · Answer

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

amistre64 · Answer

seems fair  lets clarify a bit

amistre64 · Answer

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