## patbatE21 Group Title Integrate (9 - x^2 - x -1)dy from x = -1 to x = 2 2 years ago 2 years ago

1. TuringTest Group Title

what problem exactly do you have with this integral?

2. patbatE21 Group Title

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

3. patbatE21 Group Title

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

4. TuringTest Group Title

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

5. patbatE21 Group Title

yes

6. TuringTest Group Title

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

7. patbatE21 Group Title

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

8. patbatE21 Group Title

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

9. patbatE21 Group Title

I am just having issues finding the area

10. TuringTest Group Title

let's just do the integral first, yeah?

11. patbatE21 Group Title

ok

12. patbatE21 Group Title

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

13. TuringTest Group Title

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.

14. patbatE21 Group Title

I believe that is my problem, understood

15. TuringTest Group Title

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

16. patbatE21 Group Title

Alright, I'm so far

17. TuringTest Group Title

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?

18. patbatE21 Group Title

19.2

19. TuringTest Group Title

let me try! lol

20. patbatE21 Group Title

lol ok

21. TuringTest Group Title

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

22. patbatE21 Group Title

Thank you so much

23. TuringTest Group Title

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

24. patbatE21 Group Title

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

25. TuringTest Group Title

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

26. patbatE21 Group Title

yes thats correct

27. patbatE21 Group Title

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

28. TuringTest Group Title

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 :)

29. patbatE21 Group Title

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

30. patbatE21 Group Title

Thanks once again

31. TuringTest Group Title

very welcome!