## patbatE21 4 years ago Integrate (9 - x^2 - x -1)dy from x = -1 to x = 2

1. TuringTest

what problem exactly do you have with this integral?

2. patbatE21

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

3. patbatE21

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

4. TuringTest

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

5. patbatE21

yes

6. TuringTest

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

7. patbatE21

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

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

9. patbatE21

I am just having issues finding the area

10. TuringTest

let's just do the integral first, yeah?

11. patbatE21

ok

12. patbatE21

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

13. 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.

14. patbatE21

I believe that is my problem, understood

15. TuringTest

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

16. patbatE21

Alright, I'm so far

17. 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?

18. patbatE21

19.2

19. TuringTest

let me try! lol

20. patbatE21

lol ok

21. 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

22. patbatE21

Thank you so much

23. TuringTest

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

24. patbatE21

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

25. 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

26. patbatE21

yes thats correct

27. patbatE21

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

28. 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 :)

29. patbatE21

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

30. patbatE21

Thanks once again

31. TuringTest

very welcome!