using five function values estimate

- anonymous

using five function values estimate

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- anonymous

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

- anonymous

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

- anonymous

my values maybe wrong so you might have to double check

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## More answers

- angela210793

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

- 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

why did u change 3 to -1.5?

- anonymous

really i think its quite enjoyable :)

- anonymous

its my attempt using the trapezoidal rule

- 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

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

- 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

im not from the US lol

- angela210793

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

- 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

thats my working for the trapezoidal rule

- dumbcow

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

- anonymous

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

- dumbcow

nevermind

- anonymous

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

- anonymous

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

- dumbcow

yep thats it

- anonymous

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

- dumbcow

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

- dumbcow

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

- anonymous

omg i knew i should have put brackets around them lol

- anonymous

i will try it again lol

- anonymous

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

- angela210793

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

- anonymous

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

- anonymous

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

- angela210793

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

- dumbcow

haha no love for the integrals
your welcome and

- anonymous

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

- angela210793

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

- anonymous

ill assume you mean conics lol

- angela210793

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

- anonymous

kk

- angela210793

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

- anonymous

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

- 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

I learnt another word...thanks :)

- anonymous

cool it sounds interesting

- angela210793

:)

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