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

- anonymous

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

- jamiebookeater

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- TuringTest

what problem exactly do you have with this integral?

- anonymous

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

- anonymous

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- TuringTest

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

- anonymous

yes

- TuringTest

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

- 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

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

- anonymous

I am just having issues finding the area

- TuringTest

let's just do the integral first, yeah?

- anonymous

ok

- anonymous

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

- 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

I believe that is my problem, understood

- TuringTest

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

- anonymous

Alright, I'm so far

- 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

19.2

- TuringTest

let me try! lol

- anonymous

lol ok

- 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

Thank you so much

- TuringTest

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

- anonymous

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

- 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

yes thats correct

- anonymous

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

- 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

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

- anonymous

Thanks once again

- TuringTest

very welcome!

Looking for something else?

Not the answer you are looking for? Search for more explanations.