## anonymous 5 years ago using five function values estimate

1. anonymous

$\int\limits_{-3}^{3}\sqrt{9-x ^{2}}$ using: (i)the trapezoidal rule (ii) simpsons rule

2. anonymous

the values are: x -3 -1.5 0 1.5 3 y Sqrt(18) Sqrt(45)/2 3 Sqrt(27)/2 0

3. anonymous

my values maybe wrong so you might have to double check

4. angela210793

Integrations....the thing i hate in most....:S

5. anonymous

my attempt: $\int\limits_{-3}^{3}\sqrt{9-x ^{2}}\approx \int\limits_{-3}^{-1.5}\sqrt{9-x ^{2}}+\int\limits_{-1.5}^{0}\sqrt{9-x ^{2}}+\int\limits_{0}^{1.5}\sqrt{9-x ^{2}}+\int\limits_{1.5}^{3}\sqrt{9-x ^{2}}$

6. angela210793

why did u change 3 to -1.5?

7. anonymous

really i think its quite enjoyable :)

8. anonymous

its my attempt using the trapezoidal rule

9. angela210793

it was the lowest grade i had ever taken in math....tht's y i don't like it :S:S...let me try my way plssss

10. anonymous

i have the answer using the easy way now i need to learn this method for an exam lol unfortunantely its not optional

11. angela210793

ok...I have forgotten the formulas anyway...so i can't solve it even though i tried....and i really have never seen this way of solution...maybe u in USA r smarter :P:P

12. anonymous

im not from the US lol

13. angela210793

ok..in that country from wherever u are...u seem to b smarter :P:P

14. anonymous

following from the top i get $\int\limits_{-3}^{3}\sqrt{9-x ^{2}}\approx 3/4(\sqrt{18}+\sqrt{45}/2)+3/4(3+\sqrt{45}/2)+3/4(3+\sqrt{27}/2)+3/4(\sqrt{27}/2+0)$

15. anonymous

thats my working for the trapezoidal rule

16. dumbcow

looks good where did the 3/4 come from? shouldnt it be 1/b-a

17. anonymous

the answer in the back: $\approx12.294$ whilst i get $\approx16.610$

18. dumbcow

nevermind

19. anonymous

the rule in my textbook is $\int\limits_{a}^{b}f(x)dx \approx( (b-a)/2) (f(a)+f(b))$

20. anonymous

so using this the first part is (-1.5-(-3))/2 =3/4

21. dumbcow

yep thats it

22. anonymous

but my answer is way off im dont know what im doing wrong

23. dumbcow

oh your y values are off x=-3 y=0

24. dumbcow

9-(-3)^2 =9-9

25. anonymous

omg i knew i should have put brackets around them lol

26. anonymous

i will try it again lol

27. anonymous

i have to thankyou again dumbcow you my friend are a genius :)

28. angela210793

O.o I really have never seen this before.....O.o

29. anonymous

well im in australia and we do a wide range of mathematics

30. anonymous

btw the two rules above are just approximations of the integrals theyre always abit off lol

31. angela210793

I HATE integrations..i always will..i hope tht I won't have to solve any of them in math exam :S

32. dumbcow

haha no love for the integrals your welcome and

33. anonymous

lol i actually reckon its a fun part of maths when you get it right. i hate vector geometry

34. angela210793

i hate conical lines as well (is this how u call them?) O.o

35. anonymous

ill assume you mean conics lol

36. angela210793

idk... :\$ maybe...let me google a bit plssss

37. anonymous

kk

38. angela210793

hyperbole, ellipse, parabola....these are wht i am talking abt....they r called conics?

39. anonymous

yeah they are theyre not too bad what country are you from

40. angela210793

No they are...too many formulas...then tangents.....i hate them....actually thr's nothing i like in math :P..I'm from Albania/Europe :)

41. angela210793

I learnt another word...thanks :)

42. anonymous

cool it sounds interesting

43. angela210793

:)