Question

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

Answer 1

what problem exactly do you have with this integral?

Answer 2

well the I'm actually trying to sketch a region enclosed by given curves

Answer 3

but i think there is something wrong with my integration...so far I have 9y -1/3y^3 -1/2y^2 - y

Answer 4

first off I assume you mean (9 - x^2 - x -1)dx

Answer 5

yes

Answer 6

so then you answer is correct if you replace y's with x's

Answer 7

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

Answer 8

y = x + 1, y = 9 - x^2, x = -1, x = 2

Answer 9

I am just having issues finding the area

Answer 10

let's just do the integral first, yeah?

Answer 11

ok

Answer 12

I know that I will have to take the integral [f(y) -g(y)] from c to d

Answer 13

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.

Answer 14

I believe that is my problem, understood

Answer 15

so your integral is\[\int\limits_{-1}^{2}9-x^2-x-1dx\]

Answer 16

Alright, I'm so far

Answer 17

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?

Answer 18

19.2

Answer 19

let me try! lol

Answer 20

lol ok

Answer 21

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

Answer 22

Thank you so much

Answer 23

wait a minute this is all wrong! I should have noticed sooner!

Answer 24

No its correct I just submitted it online and it is marked correct

Answer 25

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

Answer 26

yes thats correct

Answer 27

I see what you mean, but how is it still correct

Answer 28

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 :)

Answer 29

Ok, the ah-hah moments in math...such a wonderful subject

Answer 30

Thanks once again

Answer 31

very welcome!