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anonymous

  • 5 years ago

using five function values estimate

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  1. anonymous
    • 5 years ago
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    \[\int\limits_{-3}^{3}\sqrt{9-x ^{2}}\] using: (i)the trapezoidal rule (ii) simpsons rule

  2. anonymous
    • 5 years ago
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    the values are: x -3 -1.5 0 1.5 3 y Sqrt(18) Sqrt(45)/2 3 Sqrt(27)/2 0

  3. anonymous
    • 5 years ago
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    my values maybe wrong so you might have to double check

  4. angela210793
    • 5 years ago
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    Integrations....the thing i hate in most....:S

  5. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    why did u change 3 to -1.5?

  7. anonymous
    • 5 years ago
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    really i think its quite enjoyable :)

  8. anonymous
    • 5 years ago
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    its my attempt using the trapezoidal rule

  9. angela210793
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    im not from the US lol

  13. angela210793
    • 5 years ago
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    ok..in that country from wherever u are...u seem to b smarter :P:P

  14. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    thats my working for the trapezoidal rule

  16. dumbcow
    • 5 years ago
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    looks good where did the 3/4 come from? shouldnt it be 1/b-a

  17. anonymous
    • 5 years ago
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    the answer in the back: \[\approx12.294\] whilst i get \[\approx16.610\]

  18. dumbcow
    • 5 years ago
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    nevermind

  19. anonymous
    • 5 years ago
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    the rule in my textbook is \[\int\limits_{a}^{b}f(x)dx \approx( (b-a)/2) (f(a)+f(b))\]

  20. anonymous
    • 5 years ago
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    so using this the first part is (-1.5-(-3))/2 =3/4

  21. dumbcow
    • 5 years ago
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    yep thats it

  22. anonymous
    • 5 years ago
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    but my answer is way off im dont know what im doing wrong

  23. dumbcow
    • 5 years ago
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    oh your y values are off x=-3 y=0

  24. dumbcow
    • 5 years ago
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    9-(-3)^2 =9-9

  25. anonymous
    • 5 years ago
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    omg i knew i should have put brackets around them lol

  26. anonymous
    • 5 years ago
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    i will try it again lol

  27. anonymous
    • 5 years ago
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    i have to thankyou again dumbcow you my friend are a genius :)

  28. angela210793
    • 5 years ago
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    O.o I really have never seen this before.....O.o

  29. anonymous
    • 5 years ago
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    well im in australia and we do a wide range of mathematics

  30. anonymous
    • 5 years ago
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    btw the two rules above are just approximations of the integrals theyre always abit off lol

  31. angela210793
    • 5 years ago
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    I HATE integrations..i always will..i hope tht I won't have to solve any of them in math exam :S

  32. dumbcow
    • 5 years ago
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    haha no love for the integrals your welcome and

  33. anonymous
    • 5 years ago
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    lol i actually reckon its a fun part of maths when you get it right. i hate vector geometry

  34. angela210793
    • 5 years ago
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    i hate conical lines as well (is this how u call them?) O.o

  35. anonymous
    • 5 years ago
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    ill assume you mean conics lol

  36. angela210793
    • 5 years ago
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    idk... :$ maybe...let me google a bit plssss

  37. anonymous
    • 5 years ago
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    kk

  38. angela210793
    • 5 years ago
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    hyperbole, ellipse, parabola....these are wht i am talking abt....they r called conics?

  39. anonymous
    • 5 years ago
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    yeah they are theyre not too bad what country are you from

  40. angela210793
    • 5 years ago
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    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
    • 5 years ago
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    I learnt another word...thanks :)

  42. anonymous
    • 5 years ago
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    cool it sounds interesting

  43. angela210793
    • 5 years ago
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    :)

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