anonymous
  • anonymous
Integrate (9 - x^2 - x -1)dy from x = -1 to x = 2
Mathematics
jamiebookeater
  • jamiebookeater
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TuringTest
  • TuringTest
what problem exactly do you have with this integral?
anonymous
  • anonymous
well the I'm actually trying to sketch a region enclosed by given curves
anonymous
  • anonymous
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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TuringTest
  • TuringTest
first off I assume you mean (9 - x^2 - x -1)dx
anonymous
  • anonymous
yes
TuringTest
  • TuringTest
so then you answer is correct if you replace y's with x's
anonymous
  • anonymous
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
anonymous
  • anonymous
y = x + 1, y = 9 - x^2, x = -1, x = 2
anonymous
  • anonymous
I am just having issues finding the area
TuringTest
  • TuringTest
let's just do the integral first, yeah?
anonymous
  • anonymous
ok
anonymous
  • anonymous
I know that I will have to take the integral [f(y) -g(y)] from c to d
TuringTest
  • TuringTest
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.
anonymous
  • anonymous
I believe that is my problem, understood
TuringTest
  • TuringTest
so your integral is\[\int\limits_{-1}^{2}9-x^2-x-1dx\]
anonymous
  • anonymous
Alright, I'm so far
TuringTest
  • TuringTest
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?
anonymous
  • anonymous
19.2
TuringTest
  • TuringTest
let me try! lol
anonymous
  • anonymous
lol ok
TuringTest
  • TuringTest
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
anonymous
  • anonymous
Thank you so much
TuringTest
  • TuringTest
wait a minute this is all wrong! I should have noticed sooner!
anonymous
  • anonymous
No its correct I just submitted it online and it is marked correct
TuringTest
  • TuringTest
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
anonymous
  • anonymous
yes thats correct
anonymous
  • anonymous
I see what you mean, but how is it still correct
TuringTest
  • TuringTest
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 :)
anonymous
  • anonymous
Ok, the ah-hah moments in math...such a wonderful subject
anonymous
  • anonymous
Thanks once again
TuringTest
  • TuringTest
very welcome!

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