Question

@jim_thompson5910 I have a question regarding a problem almost identical to the one you helped me with, could you help out if you have time please?

Answer 1

i might be able to help

Answer 2

It's regarding the Reimann sum method, are you familiar with it?

Answer 3

go for it

Answer 4

thanks, I was doing my work using paint so I'll upload it so you can see my work, the question I'm trying to answer is: Use a Riemann sum with five subintervals of equal length (n = 5) to approximate the area of R. Choose the representative points to be the left endpoints of the subintervals.
Also, I already answered this problem for the right endpoint intervals, my question is, wouldn't using 0 or 3 end up in 0 anyway (6-2(3)) would be 0 so the right and left endpoints' sum would end up the same?

Sorry if all my writing doesn't make sense =( and i can give you my answers for the right endpoint intervals that I know i got correctly

Answer 5

ok let me have a look

Answer 6

The graph looks correct for the right endpoints (see attached)

Answer 7

for the right endpoints, you don't compute f(0)

you only compute

f(0.6)
f(1.2)
f(1.8)
f(2.4)

Answer 8

oh sry also f(3) as well

f(3) = 0, that is correct

Answer 9

ok, and for the left endpoints it'd be the same minus f(3) and the addition of f(0) which is the same thing?

Answer 10

here's what the left endpoint graph looks like

Answer 11

now you are computing

f(0)
f(0.6)
f(1.2)
f(1.8)
f(2.4)

Answer 12

5 computations because n = 5

Answer 13

Ok so I put those as x and then multiplied each by .6 and added them up

Answer 14

and got 7.2 again

Answer 15

you should get 7.2 for the right endpoints

not the left

Answer 16

let me try that again

Answer 17

oh that's right i left out the f(0) there we go

Answer 18

There we go, for some reason i was thinking that if i was using 0 it automatically turned the whole thing into 0 and was skipping it over

Answer 19

Thanks!

Answer 20

what final answers did you get

Answer 21

I got 10.8 and then for the n=10 (which I didn't mention) I got 9.9

Answer 22

10.8 is correct for the left endpoints when n = 5

Answer 23

9.9 is correct for the left endpoints when n = 10

Answer 24

Thanks again!

Answer 25

sure thing