Question

Question about Darbaux Sums. I beg of ya, take a look for me.

Answer 1

So I feel like my answer must be wrong because it is too easy. I need the lower Darbaux sum for x^3 with partitions {0, .1, .4, 1}.

Answer 2

so, the \(m_i\) for the first partition would be 0, then .001 then .064, that's it?

Answer 3

but shouldn't there be 4?

Answer 4

@jim_thompson5910, @zepdrix, any ideas?

Answer 5

@dumbcow , I can't remember, have you covered this yet?

Answer 6

@ganeshie8 be my hero?

Answer 7

hey how is it different from riemann sum ?

Answer 8

it's the precursor to riemann. It's essentially the "left handed" sum from calc II, but Maybe it's just the class throwing me off here

Answer 9

technically it is defined as:\[L(P,f)=\sum^n_{i=1} m_i\Delta x_i\]\[m_i=inf~[f(x):x_{i-1}\le x\le x_i]\]

Answer 10

i can tell you the reason there are 3 m values is because with 4 points there are 3 intervals
{x0,x1} [x1,x2] [x2,x3]

Answer 11

oh jeeze, yea, that makes sense

Answer 12

I can show you my work, the issue is I don't fully understand what the m_i are equal to.

Answer 13

m_i = inf
M_i = sup

in the ith interval

Answer 14

left sum :
http://www.wolframalpha.com/input/?i=%280.1-0%29*0%5E3%2B%280.4-0.1%29*0.1%5E3+%2B+%281-0.4%29*0.4%5E3

Answer 15

i got, m_i= 0,.001,.064

Answer 16

Hey I got the right answer!!!!

Answer 17

so I must have done it correctly! :D Thanks guys!

Answer 18

idk we both may be wrong, but based on the definition of sum it looks same as riemann sum for x^3 because min and max exist in each interval and they equal inf and sup

Answer 19

the def of riemann int has the upper and lower darbaux int. being equivalent, so maybe that is what it is

Answer 20

ohk.. do u get this for upper sum ?
http://www.wolframalpha.com/input/?i=%280.1-0%29*0.1%5E3%2B%280.4-0.1%29*0.4%5E3+%2B+%281-0.4%29*1%5E3

Answer 21

wait, I haven't done it yet

Answer 22

give me a sec

Answer 23

Okay... i think there will be difference between riemann and darbaux when the curve is concave up or down. When that happens, the left and right values will not be inf and sup respectively always

Answer 24

I got .6193 for the upper

Answer 25

i got the same!

Answer 26

yay! Thanks, I was just doubting myself since it seemed so simple