Find area bounded between f(x)=x^3-3x^2 and g(x)=x(-x^2-5x+12)

Question

anonymous · Answer

Find the intersection(s)  of the functions then determine which is the top and bottom functions.  Use a graphing calculator.... it's much faster

anonymous · Answer

I found the intersection for the first equation which was 0 and 4 but then I got stuck when doing the integral.$$\int\limits_{0}^{4}x[(2x)-(x^2-3x)] dx$$ . Im not sure if Im doing it out correctly T.T

anonymous · Answer

I don't think that's right... because according to the graphs i put into desmos, the intersect at 3 places...

anonymous · Answer

which means you'll prolly have two integrals.

tkhunny · Answer

When you find all three points of intersection, you will have to decide if you should include both bounded regions.  You will also need to think about what you are doing.

[1,4] makes no sense.  Please find the points of intersection.  No guessing.  You cannot find "the intersections" of only one equation.  You need to know where the two curves intersect each other, not where they encounter the x-axis.

anonymous · Answer

I broke up the equation I guess i'm not allowed to do that, i took an X away...T.T

tkhunny · Answer

You must solve f(x) = g(x).

anonymous · Answer

here's the graph in desmos online graphing calc...

anonymous · Answer

SO they intersect at -3, 0, & -4...

tkhunny · Answer

How did you get that?  Not quite.  Give it another go.

anonymous · Answer

0,3 ??

tkhunny · Answer

Why are you guessing?  Please show the equation you are trying to solve and how you are trying to solve it.  Trouble with algebra only makes calculus harder.