anonymous
  • anonymous
using five function values estimate
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\int\limits_{-3}^{3}\sqrt{9-x ^{2}}\] using: (i)the trapezoidal rule (ii) simpsons rule
anonymous
  • anonymous
the values are: x -3 -1.5 0 1.5 3 y Sqrt(18) Sqrt(45)/2 3 Sqrt(27)/2 0
anonymous
  • anonymous
my values maybe wrong so you might have to double check

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angela210793
  • angela210793
Integrations....the thing i hate in most....:S
anonymous
  • anonymous
my attempt: \[\int\limits_{-3}^{3}\sqrt{9-x ^{2}}\approx \int\limits_{-3}^{-1.5}\sqrt{9-x ^{2}}+\int\limits_{-1.5}^{0}\sqrt{9-x ^{2}}+\int\limits_{0}^{1.5}\sqrt{9-x ^{2}}+\int\limits_{1.5}^{3}\sqrt{9-x ^{2}}\]
angela210793
  • angela210793
why did u change 3 to -1.5?
anonymous
  • anonymous
really i think its quite enjoyable :)
anonymous
  • anonymous
its my attempt using the trapezoidal rule
angela210793
  • 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
anonymous
  • anonymous
i have the answer using the easy way now i need to learn this method for an exam lol unfortunantely its not optional
angela210793
  • 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
anonymous
  • anonymous
im not from the US lol
angela210793
  • angela210793
ok..in that country from wherever u are...u seem to b smarter :P:P
anonymous
  • anonymous
following from the top i get \[\int\limits_{-3}^{3}\sqrt{9-x ^{2}}\approx 3/4(\sqrt{18}+\sqrt{45}/2)+3/4(3+\sqrt{45}/2)+3/4(3+\sqrt{27}/2)+3/4(\sqrt{27}/2+0)\]
anonymous
  • anonymous
thats my working for the trapezoidal rule
dumbcow
  • dumbcow
looks good where did the 3/4 come from? shouldnt it be 1/b-a
anonymous
  • anonymous
the answer in the back: \[\approx12.294\] whilst i get \[\approx16.610\]
dumbcow
  • dumbcow
nevermind
anonymous
  • anonymous
the rule in my textbook is \[\int\limits_{a}^{b}f(x)dx \approx( (b-a)/2) (f(a)+f(b))\]
anonymous
  • anonymous
so using this the first part is (-1.5-(-3))/2 =3/4
dumbcow
  • dumbcow
yep thats it
anonymous
  • anonymous
but my answer is way off im dont know what im doing wrong
dumbcow
  • dumbcow
oh your y values are off x=-3 y=0
dumbcow
  • dumbcow
9-(-3)^2 =9-9
anonymous
  • anonymous
omg i knew i should have put brackets around them lol
anonymous
  • anonymous
i will try it again lol
anonymous
  • anonymous
i have to thankyou again dumbcow you my friend are a genius :)
angela210793
  • angela210793
O.o I really have never seen this before.....O.o
anonymous
  • anonymous
well im in australia and we do a wide range of mathematics
anonymous
  • anonymous
btw the two rules above are just approximations of the integrals theyre always abit off lol
angela210793
  • angela210793
I HATE integrations..i always will..i hope tht I won't have to solve any of them in math exam :S
dumbcow
  • dumbcow
haha no love for the integrals your welcome and
anonymous
  • anonymous
lol i actually reckon its a fun part of maths when you get it right. i hate vector geometry
angela210793
  • angela210793
i hate conical lines as well (is this how u call them?) O.o
anonymous
  • anonymous
ill assume you mean conics lol
angela210793
  • angela210793
idk... :$ maybe...let me google a bit plssss
anonymous
  • anonymous
kk
angela210793
  • angela210793
hyperbole, ellipse, parabola....these are wht i am talking abt....they r called conics?
anonymous
  • anonymous
yeah they are theyre not too bad what country are you from
angela210793
  • 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 :)
angela210793
  • angela210793
I learnt another word...thanks :)
anonymous
  • anonymous
cool it sounds interesting
angela210793
  • angela210793
:)

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