Question

using five function values estimate

Answer 1

\[\int\limits_{-3}^{3}\sqrt{9-x ^{2}}\]

using:

(i)the trapezoidal rule
(ii) simpsons rule

Answer 2

the values are:

x -3 -1.5 0 1.5 3
y Sqrt(18) Sqrt(45)/2 3 Sqrt(27)/2 0

Answer 3

my values maybe wrong so you might have to double check

Answer 4

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

Answer 5

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

Answer 6

why did u change 3 to -1.5?

Answer 7

really i think its quite enjoyable :)

Answer 8

its my attempt using the trapezoidal rule

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

im not from the US lol

Answer 13

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

Answer 14

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

Answer 15

thats my working for the trapezoidal rule

Answer 16

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

Answer 17

the answer in the back:
\[\approx12.294\]

whilst i get \[\approx16.610\]

Answer 18

nevermind

Answer 19

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

Answer 20

so using this the first part is

(-1.5-(-3))/2 =3/4

Answer 21

yep thats it

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

omg i knew i should have put brackets around them lol

Answer 26

i will try it again lol

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

haha no love for the integrals
your welcome and

Answer 33

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

Answer 34

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

Answer 35

ill assume you mean conics lol

Answer 36

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

Answer 37

kk

Answer 38

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

Answer 39

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

Answer 40

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 :)

Answer 41

I learnt another word...thanks :)

Answer 42

cool it sounds interesting

Answer 43

:)