Question

Let f(x) = 4 - 12/x^2. Calculate the lower and upper sum estimates of the area under the curve over the interval [2,5] using subintervals of width ½.

Answer 1

i got a hint from my teacher:
Technology hints: A graph can be helpful in checking to see if your answers are reasonable. Since we are getting estimates, it would be appropriate to use a calculator or spreadsheet to do the calculations accurate to four decimal places, then round your final upper and lower sum to three.

Answer 2

Zubhanwc3 is correct. We actually just did finding the area under a curve in my Calculus class. I'm going to graph it in my graphing calculator and see the graph that we are dealing with.

Answer 3

can i get help for my question then ^^?

Answer 4

Oh lol you replied to your own message. Okay :)

Answer 5

Is that 4 - (12/x^2) ? ? ?

Answer 6

yes

Answer 7

You're using Riemann sum right? The old fashion way of computing an integral?

Answer 8

i think so

Answer 9

Ooh you get an interesting graph from that. Luckily between 2 and 5 it is all positive so there will be no negative area. Yes Luigi this is Riemann sums.

Answer 10

I'm going to set my table for 1/2 width, and then check the points. Should I check from the left, middle, or right?

Answer 11

@zubhanwc3 The default is middle but I just want to make sure. I learned left first and middle last

Answer 12

i have no idea T_T
im not supposed to do riemann sum, but apparently i am T_T

Answer 13

the lesson after this one is about riemann sums.

Answer 14

Do you happen to be using a Calculus textbook with a weird looking circle type thing on the cover?

Answer 15

yes. Calculus graphical, numerical and algebraic. fourth edition

Answer 16

I have 9th edition and it's just AP Edition. I'm sorry I just don't understand what your teacher or textbook is asking from you.

Answer 17

mine also says ap edition. if you google my book, you can see the cover.

Answer 18

alrite then, wats the riemann sum method? i might as well get the problem done with T_T.

Answer 19

I could help, but I have to go :(

Answer 20

Okay yeah it is different, but the section for me before Rieman sums is just titled "Area."

It uses changeofx = b-a/n

Does that look familier?

Answer 21

o
we got same thing:P im on the section titled area.

Answer 22

and no, that doesn't look familiar.

Answer 23

are you in ap calc ab?

Answer 24

Yeah

Answer 25

connections acad?

Answer 26

wait, different book, so i guess not:P

Answer 27

how do i figure out the number of rectangles?

Answer 28

You find the number of triangles from the numbers.

You are looking between the x points of 2 and 5

5-2 = 3

Now you have to do 3/1/2

That gives you 6 different rectangles.

Answer 29

by plugging it in, my estimated area should be 8.4286, right? so would that be the answer?

Answer 30

im really confused about the upper and lower sum estimates part of it >.<

Answer 31

Lower sums is measuring it from the left. Upper sums is from the right
That's what I was trying to ask you XD

Answer 32

yay, so i gotta get 2 estimates from both, well not a problem T_T

Answer 33

I gotta go but good luck. I hope that helped.