Find the area of the region bounded by the graphs of the given equations.
y=5x-x^2
y=x

Question

Find the area of the region bounded by the graphs of the given equations.
y=5x-x^2
y=x

luigi0210 · Answer

I think we need to fins the points of intersection first, right?

lukecrayonz · Answer

Indeed! :)

kainui · Answer

Show us your best attempt at finding them!

luigi0210 · Answer

So we start with:
x=5x-x^2

Now go :3

lukecrayonz · Answer

So (0,0) and (4,4)

luigi0210 · Answer

Yea xD
So now we have our limits.

lukecrayonz · Answer

So the range is [0,4]

lukecrayonz · Answer

So then what? I mean Do you do [0,4] integral for both then add? Is that it?

luigi0210 · Answer

We set up the integrals, we subtract the graph that is larger or taller from the smaller one.. so as we see here: It's 5x-x^2 and then comes x

The integral would be setup as:
$$\LARGE \int\limits_{0}^{4}~(5x-x^2)~dx-\int\limits_{0}^{4}x~dx$$

lukecrayonz · Answer

That makes sense:) Thank you! Also, could you quickly do this? I'm getting 11894.27 but the answer is apparently 6917.32 http://gyazo.com/c0a17f2ec5f0e0b76632ad5604d28913

luigi0210 · Answer

Still integration right? Or is it average value? o_O

lukecrayonz · Answer

Avg value I guess :O

luigi0210 · Answer

Hmm, hold on, let me get someone @dan815

lukecrayonz · Answer

Daaaaaaan! :D

lukecrayonz · Answer

@Isaiah.Feynman

luigi0210 · Answer

Maybe open a new question? I think it'd be easier for then to see it >.<

luigi0210 · Answer

them

isaiah.feynman · Answer

Your problem is solved already. :D