Integrate (9 - x^2 - x -1)dy from x = -1 to x = 2

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Integrate (9 - x^2 - x -1)dy from x = -1 to x = 2

Mathematics
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what problem exactly do you have with this integral?
well the I'm actually trying to sketch a region enclosed by given curves
but i think there is something wrong with my integration...so far I have 9y -1/3y^3 -1/2y^2 - y

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first off I assume you mean (9 - x^2 - x -1)dx
yes
so then you answer is correct if you replace y's with x's
the actual question is " Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region
y = x + 1, y = 9 - x^2, x = -1, x = 2
I am just having issues finding the area
let's just do the integral first, yeah?
ok
I know that I will have to take the integral [f(y) -g(y)] from c to d
It's f(x)-g(x) I think you are having a problem keeping track of variables, remember y=f(x), so f(y) is something different and undefined here.
I believe that is my problem, understood
so your integral is\[\int\limits_{-1}^{2}9-x^2-x-1dx\]
Alright, I'm so far
your answer is right replaced with x's\[9x-{1\over3}x^3-{1\over2}x^2-x\]evaluated from -1 to 2, what do you get?
19.2
let me try! lol
lol ok
Sorry 19.5 Just the evaluation, right? As you see I hate that too, here's a site, if you don't already know it that's good for that. http://www.wolframalpha.com/ and here's your particular problem http://www.wolframalpha.com/input/?i=Integrate+%289+-+x%5E2+-+x+-1%29dx+from+-1+to+2
Thank you so much
wait a minute this is all wrong! I should have noticed sooner!
No its correct I just submitted it online and it is marked correct
did you mean it as you typed it? 9 - x^2 - x -1 are you mot missing an x? because 9-1=8 so the integration we di is wrong
yes thats correct
I see what you mean, but how is it still correct
Okay it's not ALL wrong, but the way wee did it is silly, it may be right, but we failed to notice that \[9 - x^2 - x -1=8-x^2-x\] So we integrated an extra term. It is important to see shortcuts like that, so at least look for those in the future :)
Ok, the ah-hah moments in math...such a wonderful subject
Thanks once again
very welcome!

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