I need help with one question of Calculus 1.

- Jaweria

I need help with one question of Calculus 1.

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- anonymous

what is your question?

- Jaweria

My question is this: USe 5 rectangles to estimate the area under the graph of: f(x) = 2x^3+2x-5. from x=2 to x=7

- Jaweria

And also tell whether your estimate is an over or an upper estimate, explain why?

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- anonymous

oh you are doing reimann sums? let me do some work, give me a second

- Jaweria

ok thx

- Jaweria

if you can check with me that I got my 5 rectangles: 35, 93, 193, -92, -128 are they right?

- anonymous

hmmmmm im gonna draw up the graph so that we know we have the same thing|dw:1366346945142:dw|
That is the graph that i have, roughly at least, is that the same thing that you are working with?

- Jaweria

yeah

- Jaweria

but can you please check my numbers plzz

- anonymous

i punched this into my calculator, and the base for each rectangle would be 1, because you are using 5 rectangles, and the difference between 7 and 2 is 5. so you are basicallly looking at the height, but i got 15, 55, 131, 255, and 439. i dont see how you could get any negative because the line is going up

- Jaweria

yeah i got that too but I m saying that arent we suppose to add up those rectangles?

- Jaweria

so whats my answer basically?

- Jaweria

Someone plzz help me

- anonymous

intervals =b-a/n (7-2)/5 =1

- anonymous

yea, you just add what you got for the areas, so 15+55+131+255+439=839. and it would be an under estimate because it is a left side reimann sum. meaning that the left corner of the boxes hit the line

- Jaweria

i thought its over estimate because its increasing

- anonymous

|dw:1366348904077:dw|
that isnt to scale, but that is the basic idea of what is going on

- Jaweria

oh thx

- anonymous

no problem

- Jaweria

one more plzz

- anonymous

shoot

- Jaweria

if you dont mind

- Jaweria

ok

- Jaweria

Use 5 rectangles to esitmate the area under the graph: y=x^3-10x^2+27x-18

- Jaweria

from 1

- Jaweria

|dw:1366349539104:dw|

- anonymous

ok so your graph is going to look like:
|dw:1366349701319:dw|
roughly of course.

- Jaweria

its ok

- Jaweria

so how am I actually going to solve this

- anonymous

are you supposed to use 5 boxes again?

- Jaweria

yeah its says 5 rectangles

- anonymous

does this problem have the same basis as the other problem you posted? meaning you are just looking for rectangles to find the area under the graph? ok, 5 rectangles

- Jaweria

yeah

- Jaweria

and it also gives you from where to where

- Jaweria

which is this |dw:1366349945211:dw|

- anonymous

right, so this again is the same difference as the other problem, (5) so each will have the same base length of 1

- Jaweria

ok

- Jaweria

can we work on this together little bit ?

- Jaweria

If you dont mind?

- anonymous

yes of course we can. how would you like to do that? i would like to help you in the best way that suits you

- Jaweria

can you first show me how to get the value for the 1st rectangle?

- anonymous

yes, i personally am using a graphing calculator because i find it is the easiest way to do it. are you using the same, or are you trying to do this by hand?

- anonymous

@Jaweria

- Jaweria

hand

- Jaweria

we are not allow to use calculator

- anonymous

ok, that is fine, that just means that we are going to have to find the value for y at every point. and our points are going to be 1,2,3,4,5,6. do you think you can solve for y using the equation for these six points? and would you like to solve them on your own, and then post them, and we can compare values?

- Jaweria

ok so first I m using 1 for my y

- anonymous

nope, we are gonna be solving for y, so we are going to plug 1,2,3,4,5 and 6 in for x into the equation

- Jaweria

oh ok

- anonymous

so solve for y, using those six values and let me know what you get

- Jaweria

so let me get their values then I ll tell you

- Jaweria

alright

- anonymous

ok, and solve for 1,2,3,4,5 that will give us 5 rectangles

- anonymous

did you get the values?

- Jaweria

so far I got 10,4,0

- anonymous

hmmmm, that first one isnt correct
try it again

- Jaweria

ok

- Jaweria

its 0

- anonymous

that is correct, now go ahead and fine the y value for 4 and 5

- Jaweria

ok

- anonymous

did you solve for them? sorry if i am rushing you, i dont mean to be

- anonymous

@jaweria

- Jaweria

I m sorry my stupid laptop is giving me tough time

- anonymous

its all good no worries

- Jaweria

I got -10

- Jaweria

is that right?

- anonymous

you need, two more values, but -10 is not correct, you are going to need to solve for 4 and 5. go ahead and do that and let me know what you get

- Jaweria

I got -6 for 4

- Jaweria

and -8 for 5

- anonymous

that is correct. now we need to find the area of each of those rectangles. and the base of each of those rectangles is 1, so the area of each of those rectangles will be equal to the value, so we have 0,4,0,-6,-8. so now all we need to do is add those values.

- anonymous

so A=0+4+0-6-8. what do you get for area?

- Jaweria

yeah i got that too all of them

- Jaweria

but then how am i suppose to find an area
add them up?

- Jaweria

and then divide it by some number?

- anonymous

we found that the base of each of those rectangles would be 1. and the area of a rectangle is b*h. we found the height by finding the y. so in essence you are multplying each of the values we found (0,4,0,-6,-8) by one, but they will equal the values themselves.
so what wer are actually doing is A=0(1)+4(1)+0(1)-6(1)-8(1)

- anonymous

can you solve for area from that?

- Jaweria

oh ok

- anonymous

what do you get for area?

- Jaweria

yeah its -10

- Jaweria

I m still getting -10

- anonymous

thta is right. is that what you were reffering to earlier when you said -10?

- Jaweria

yup

- anonymous

oh im extremely sorry, i did not realize that is what you were referrring to. i really do feel bad, im sorry. but yes it is -10, and it would still be an under estimate because we used a left corner triangle

- Jaweria

its ok :)

- Jaweria

so thats my answer ?

- anonymous

haha ok. well im glad we went through it still. yes the area under the graph by the estimate of 5 rectangles is -10. do you understand how we came to the answer?

- Jaweria

yup I completely did thanks a lot:)

- anonymous

absolutely no problem!

- Jaweria

I should go to sleep now its really late take care bye.

- anonymous

i hear ya haha. take care and good luck in your studies

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