Question

Riemann sum problem..left and right. Posting

Answer 1

if someone could walk me through this i'd appreciate it. I know that you would take the width times the left endpoints' y values are at each x...but every time I calculate it I don't get the right answer ><

i used these x for the left: 3, 3.5, 4, 4.5, 5.5, 6, 6.5 and then got the y values and multiplied those by (1/2) because that is the width.

Answer 2

what y values did you get?

Answer 3

umm well i plugged them into my calcator and melted by (1/2) right away so those values were as follows: 2.5 + 3.15 + 3.6 + 4.05 + 4.5 + 4.95 + 5.4 + 5.85

Answer 4

ok im hear it is @lsherron

Answer 5

this is what geogebra produces

Answer 6

lo siento déjame etiquetar a alguien que sé paseíto puede ayudarle.

Answer 7

De acuerdo?

Answer 8

no lo siento no hablo mucho español. Pero gracias

Answer 9

ok and then i multiply those values by 1/2? right?

Answer 10

add them up, then multiply by 1/2

Answer 11

you can multiply them all by 1/2, then add, but it's easier to add then multiply in my opinion

Answer 12

@dan815 @Preetha

Answer 13

got it!

Answer 14

thay will help you i can count on it

Answer 15

so for the next one we use the right side so all the values from 3.5 to 7?

Answer 16

correct

Answer 17

ok but do u understand the last part

Answer 18

look at part 1

what do you notice about the left rectangles from x = 3 to x = 5 ?

Answer 19

sorry my laptop died on me :(

um idk tho...is it just the way that the rectangles are placed?

Answer 20

all of the left endpoint rectangles are under the curve from x = 3 to x = 5, no?

Answer 21

yes

Answer 22

so the left endpoint riemann sum is an under approximation of the actual integral from 3 to 5

Answer 23

oh i mean the last picture (part 3)

Answer 24

yeah I'm referring to that

Answer 25

in contrast the right endpoint rectangles are above the curve, so it's an over approximation

Answer 26

ok so i write that? I'm confused about the layout haha

Answer 27

meaning

\[\Large L_{4} \le \int_{3}^{5} f(x) dx \le R_{4}\]

L4 means "left endpoint rectangles, n = 4"
R4 means "right endpoint rectangles, n = 4"
the rectangles are both from a = 3 to b = 5

Answer 28

\[\Large R_{4} \le \int_{5}^{7} f(x) dx \le L_{4}\]

the rectangles are both from a = 5 to b = 7

Answer 29

oh wait, we have actual numbers to work with. I'm not thinking lol

Answer 30

For a = 3 to b = 5, what is the value of L4?

Answer 31

lol ok sorry what is L4

Answer 32

L4 is the left endpoint rectangles (4 of them) areas added up

in this case, a = 3 and b = 5

so the left most edge is at 3, the right most edge is at 5

Answer 33

so it's like part 1 but we don't go from 3 to 7

we go from 3 to 5

Answer 34

ohhh ok.. lol so how would i input answers?

Answer 35

add up the y values from x = 3 to x = 4.5

then multiply by 1/2

Answer 36

ok then i put that value on the right side of the integral in the middle?

Answer 37

what value did you get?

Answer 38

9.25 actually

Answer 39

so that is an underestimate of the integral from 3 to 5

Answer 40

\[\Large 9.25 \le \int_{3}^{5} f(x) dx \le R_{4}\]

Answer 41

yes i understand

Answer 42

do you know how to find R4?

Answer 43

oh so the Right side.?

Answer 44

the right endpoint rectangles from a = 3 to b = 5

Answer 45

11.75?

Answer 46

no 9.65

Answer 47

yeah 9.65

Answer 48

\[\Large 9.25 \le \int_{3}^{5} f(x) dx \le 9.65\]

Answer 49

and you'll do the same for a = 5 to a = 7

Answer 50

ok so for the next one it would be from 5 to 6.5 and divide by 1/2? (for the left side

Answer 51

multiply by 1/2

Answer 52

but yes you have the right idea