Question

Riemann Sum...

Answer 1

I got as far as figuring out delta x to be 2/n

Answer 2

And what I preceived the second one to be \[(\frac{ 12i ^{2} }{ n ^{2} } + \frac{ 40i }{ n }) (\frac{ 2 }{ n })\]

Answer 3

ah its been so long since ive done this. can you jog my memory when it says the general formulae of \[x _{i}\]

Answer 4

You mean the part where \[x _{i}=0+i \Delta x\]?

Answer 5

yeah is that what the formulae is for that bit? ah i should know this cause its so fundemental to calc but i only vaguely remember haha

Answer 6

perhaps @IrishBoy123 can help he's a bit of a god

Answer 7

Aha, I think so. There was a previous question regarding Riemann Sum but tackling it from the left and the question is a bit different. I could potentially upload that and tell you what I got for if you'd prefer it.

Answer 8

perhaps that could help
but since we have n divisions, then our partitions are 0, \[\Delta x, 2\Delta x, ... , (n-2) \Delta x, (n-1) \Delta x, \]

Answer 9

2

Answer 10

hmm that won't help

Answer 11

for right hand side,
\[\Delta x \left[ f( a + \Delta x ) + f(a + 2 \Delta x)+\cdots+f(b) \right].\]

Answer 12

where a=0 b=2

Answer 13

that is your approx function if you do the right end method

Answer 14

it looks like they are leading you the way step by step, i'm just unsure what it means by the general formulae of x(i)

Answer 15

is this like a web this where you enter an answer and you can see if its right or wrong?

Answer 16

It isn't a web thing, more just like an extended question that the professor gave at the end of lecture. I've been trying to follow a link that my friend shared with me on Facebook. It seems pretty legit despite being a yahoo answer source, but even then as I say that it was hard for me to get my head around the answer: https://answers.yahoo.com/question/index?qid=20110910015823AARrDF4

Answer 17

sweet, i have something to work with now

Answer 18

Hope that it'd be more useful to you than it was to me! :P

Answer 19

https://gyazo.com/ce50525553b52e9dbd904fb7970fc13a

i'm with you on this

Answer 20

if that helps :p

Answer 21

ok so x(i) is defined as \[x _{i}=i \Delta x\]

Answer 22

yes

Answer 23

\[x_i = i \frac{2}{n}\]

Answer 24

you know \[\Delta x= \frac{ 2 }{ n }\]

Answer 25

yep!^^

Answer 26

follow @Clarence

Answer 27

i'm pretty rusty on this too so careful with the symbology but i worked it through and got 48 both ways for the integral

at least that means we are on track

Answer 28

haha

Answer 29

I'm understanding what you two are saying so far so that's good I suppose. :p

Answer 30

now since you know {x _{i}\]

Answer 31

\[x _{i}\]

Answer 32

sub that into the x variables in the function 3x^2+20x

Answer 33

@chris00 yes!

Answer 34

so you get \[3x _{i}^2+20x _{i}\]

Answer 35

can you do this long hand @Clarence

Answer 36

its bringing back memories now ahaha

Answer 37

you should get \[\frac{ 12i^2 }{ n^2 }+\frac{ 60i }{ n }\]

Answer 38

I think I got 40 rather than 60 for that bit...

Answer 39

\[f(x_i) = 3 (\frac{2i}{n})^2 + 20 (\frac{2i}{n})\]

Answer 40

hahah opps

Answer 41

let's agree it before we move on :-)

Answer 42

i can math

Answer 43

:P

Answer 44

Aha, we all make these mistakes :)

Answer 45

so we are here, right??

\[\frac{ 12i^2 }{ n^2 }+\frac{ 40i }{ n }\]

Answer 46

yeah so \[f(x _{i})=\frac{ 12i^2 }{ n^2 }+\frac{ 40i }{ n }\]

Answer 47

yes, i forgot the \(f(x_i)\)

cool

next bit

Answer 48

\[f(x _{i}) \Delta x=(\frac{ 12i^2 }{ n^2 }+\frac{ 40i }{ n }) \Delta x\]

Answer 49

and you know what delta x is right clarence?

Answer 50

exellent!

Answer 51

Yup, so just input that into the equation to get 2/n at the right end

Answer 52

and the answer is???!!!!

Answer 53

simply sub 2/n into delta x to get:

\[f(x _{i}) \Delta x=(\frac{ 12i^2 }{ n^2 }+\frac{ 40i }{ n })(\frac{ 2 }{ n })\]

Answer 54

which is what you got!

Answer 55

Before I got stuck, yes ;)

Answer 56

now we approximate the area

Answer 57

my go!!

\[f(x _{i}) \Delta x=\frac{ 24i^2 }{ n^3 }+\frac{ 80i }{ n^2 }\]

Answer 58

do we agree that?!

Answer 59

yep!

Answer 60

cool, now for the real fun bit!

Answer 61

\[A _{app}\approx \sum_{i=0}^{n}(f(x _{i}) \Delta x\]

Answer 62

i think thats by definition...

Answer 63

somthing like that. this is not your graph but it just shows that the area approximation of one rectangle is Delta x multiplied by the function governing the rectangle