Jaweria
  • Jaweria
I need help with one question of Calculus 1.
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
what is your question?
Jaweria
  • 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
  • Jaweria
And also tell whether your estimate is an over or an upper estimate, explain why?

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anonymous
  • anonymous
oh you are doing reimann sums? let me do some work, give me a second
Jaweria
  • Jaweria
ok thx
Jaweria
  • Jaweria
if you can check with me that I got my 5 rectangles: 35, 93, 193, -92, -128 are they right?
anonymous
  • 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
  • Jaweria
yeah
Jaweria
  • Jaweria
but can you please check my numbers plzz
anonymous
  • 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
  • Jaweria
yeah i got that too but I m saying that arent we suppose to add up those rectangles?
Jaweria
  • Jaweria
so whats my answer basically?
Jaweria
  • Jaweria
Someone plzz help me
anonymous
  • anonymous
intervals =b-a/n (7-2)/5 =1
anonymous
  • 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
  • Jaweria
i thought its over estimate because its increasing
anonymous
  • anonymous
|dw:1366348904077:dw| that isnt to scale, but that is the basic idea of what is going on
Jaweria
  • Jaweria
oh thx
anonymous
  • anonymous
no problem
Jaweria
  • Jaweria
one more plzz
anonymous
  • anonymous
shoot
Jaweria
  • Jaweria
if you dont mind
Jaweria
  • Jaweria
ok
Jaweria
  • Jaweria
Use 5 rectangles to esitmate the area under the graph: y=x^3-10x^2+27x-18
Jaweria
  • Jaweria
from 1
Jaweria
  • Jaweria
|dw:1366349539104:dw|
anonymous
  • anonymous
ok so your graph is going to look like: |dw:1366349701319:dw| roughly of course.
Jaweria
  • Jaweria
its ok
Jaweria
  • Jaweria
so how am I actually going to solve this
anonymous
  • anonymous
are you supposed to use 5 boxes again?
Jaweria
  • Jaweria
yeah its says 5 rectangles
anonymous
  • 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
  • Jaweria
yeah
Jaweria
  • Jaweria
and it also gives you from where to where
Jaweria
  • Jaweria
which is this |dw:1366349945211:dw|
anonymous
  • 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
  • Jaweria
ok
Jaweria
  • Jaweria
can we work on this together little bit ?
Jaweria
  • Jaweria
If you dont mind?
anonymous
  • 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
  • Jaweria
can you first show me how to get the value for the 1st rectangle?
anonymous
  • 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
  • anonymous
@Jaweria
Jaweria
  • Jaweria
hand
Jaweria
  • Jaweria
we are not allow to use calculator
anonymous
  • 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
  • Jaweria
ok so first I m using 1 for my y
anonymous
  • 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
  • Jaweria
oh ok
anonymous
  • anonymous
so solve for y, using those six values and let me know what you get
Jaweria
  • Jaweria
so let me get their values then I ll tell you
Jaweria
  • Jaweria
alright
anonymous
  • anonymous
ok, and solve for 1,2,3,4,5 that will give us 5 rectangles
anonymous
  • anonymous
did you get the values?
Jaweria
  • Jaweria
so far I got 10,4,0
anonymous
  • anonymous
hmmmm, that first one isnt correct try it again
Jaweria
  • Jaweria
ok
Jaweria
  • Jaweria
its 0
anonymous
  • anonymous
that is correct, now go ahead and fine the y value for 4 and 5
Jaweria
  • Jaweria
ok
anonymous
  • anonymous
did you solve for them? sorry if i am rushing you, i dont mean to be
anonymous
  • anonymous
@jaweria
Jaweria
  • Jaweria
I m sorry my stupid laptop is giving me tough time
anonymous
  • anonymous
its all good no worries
Jaweria
  • Jaweria
I got -10
Jaweria
  • Jaweria
is that right?
anonymous
  • 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
  • Jaweria
I got -6 for 4
Jaweria
  • Jaweria
and -8 for 5
anonymous
  • 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
  • anonymous
so A=0+4+0-6-8. what do you get for area?
Jaweria
  • Jaweria
yeah i got that too all of them
Jaweria
  • Jaweria
but then how am i suppose to find an area add them up?
Jaweria
  • Jaweria
and then divide it by some number?
anonymous
  • 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
  • anonymous
can you solve for area from that?
Jaweria
  • Jaweria
oh ok
anonymous
  • anonymous
what do you get for area?
Jaweria
  • Jaweria
yeah its -10
Jaweria
  • Jaweria
I m still getting -10
anonymous
  • anonymous
thta is right. is that what you were reffering to earlier when you said -10?
Jaweria
  • Jaweria
yup
anonymous
  • 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
  • Jaweria
its ok :)
Jaweria
  • Jaweria
so thats my answer ?
anonymous
  • 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
  • Jaweria
yup I completely did thanks a lot:)
anonymous
  • anonymous
absolutely no problem!
Jaweria
  • Jaweria
I should go to sleep now its really late take care bye.
anonymous
  • anonymous
i hear ya haha. take care and good luck in your studies

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