Question

@Michele_Laino @DanJS

Answer 1

yeah , didn't i do one of these with you yesterday , or was that someone else?

Answer 2

uhh im not sure

Answer 3

pretty sure we did, but would you be able to explain it step by step again please? (: @DanJS

Answer 4

\[\lim_{i \rightarrow \infty} \sum_{i=1}^{n}f(a + i \Delta x)(\Delta x)\]

Answer 5

\[\Delta x = \frac{ b-a }{ n }\]

Answer 6

interval [a,b]

Answer 7

here [a,b] = [0,3] and
n = 6

Answer 8

f(x) = x^3 - 6x

Answer 9

got it so far!

Answer 10

so

\[\Delta x = \frac{ 3-0 }{ n } = \frac{ 3 }{ 6 } = 2\]

Answer 11

\[f(0 + i \Delta x) = f(i \Delta x)= f(2i)\]

Answer 12

\[\sum_{i=1}^{6}f(2i)(2)\]

Answer 13

\[\sum_{i=1}^{6} [(2i)^3 - 6(2i)]*(2)\]

Answer 14

add all those up for i=1 to i=6

Answer 15

the difference between the right and left points is that i starts at zero or i starts at 1

Answer 16

wait thats it?

Answer 17

you have to let i=1,2,3,4,5,6 and add all those up

Answer 18

but it says Give three decimal places in your answer.

Answer 19

yeah for instance i=1
[ (2*1)^3 - 6(2*1) ] * (2) = ?

Answer 20

then let i=2, i=3 ...all up to i = 6 and add those numbers together.

Answer 21

shoot, n = 6 so delta x is 1/2 not 2

Answer 22

wee need to go back

Answer 23

\[\sum_{i=1}^{6}[f(\frac{ i }{ 2 }) * (\frac{ 1 }{ 2 })]\]

Answer 24

\[\sum_{i=1}^{6}[ (\frac{ i }{ 2 })^3 - 6(\frac{ i }{ 2 })]*[\frac{ 1 }{ 2] } \]

Answer 25

I got \[\frac{ -63 }{ 16 }\]

Answer 26

which makes sense, because the graph is below the x axis for most of the interval from 0 to 3

Answer 27

yeah , i think so

Answer 28

I havent done these in a while, i just learned it as i went, so take it as it is. lol

Answer 29

ahhah its okay thank you

Answer 30

it looks good going back through it, so

Answer 31

\[\Delta x [ f(a+ \Delta x) + f(a+2 \Delta x) + f(a+3 \Delta x) + ... + f(b)]\]

Answer 32

where

\[\Delta X = \frac{ 1 }{ 2 }\]
and
[a,b] = [0,3]

Answer 33

that is the first part written out, you have to figure out f(x) for those values and add them

1/2 ( f(1/2) + f(2/2) + f(3/2) + f(4/2) + f(5/2) + f(6/2) + f(3))

Answer 34

the sum represents the approximation of the area between the graph of f(x) and the x axis. The larger you let n be, the better the approximation. As n goes to infinity, the sum approaches the integral of f(x) or the exact area between the curve and the x axis.

Answer 35

re-find the sum using the last thing i wrote, it may be different, half of all those f(x) added up

Answer 36

f of 1/2 , 2/2, 3/2, 4/2, 5/2, and 6/2

Answer 37

f(x) = x^3 - 6x