Jaweria
I need help with one question of Calculus 1.
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dave0616
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what is your question?
Jaweria
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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
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And also tell whether your estimate is an over or an upper estimate, explain why?
dave0616
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oh you are doing reimann sums? let me do some work, give me a second
Jaweria
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ok thx
Jaweria
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if you can check with me that I got my 5 rectangles: 35, 93, 193, -92, -128 are they right?
dave0616
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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
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yeah
Jaweria
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but can you please check my numbers plzz
dave0616
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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
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yeah i got that too but I m saying that arent we suppose to add up those rectangles?
Jaweria
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so whats my answer basically?
Jaweria
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Someone plzz help me
jojo921
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intervals =b-a/n (7-2)/5 =1
dave0616
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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
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i thought its over estimate because its increasing
dave0616
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|dw:1366348904077:dw|
that isnt to scale, but that is the basic idea of what is going on
Jaweria
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oh thx
dave0616
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no problem
Jaweria
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one more plzz
dave0616
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shoot
Jaweria
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if you dont mind
Jaweria
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ok
Jaweria
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Use 5 rectangles to esitmate the area under the graph: y=x^3-10x^2+27x-18
Jaweria
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from 1<equal to x <equalt to 6
Jaweria
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|dw:1366349539104:dw|
dave0616
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ok so your graph is going to look like:
|dw:1366349701319:dw|
roughly of course.
Jaweria
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its ok
Jaweria
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so how am I actually going to solve this
dave0616
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are you supposed to use 5 boxes again?
Jaweria
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yeah its says 5 rectangles
dave0616
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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
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yeah
Jaweria
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and it also gives you from where to where
Jaweria
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which is this |dw:1366349945211:dw|
dave0616
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right, so this again is the same difference as the other problem, (5) so each will have the same base length of 1
Jaweria
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ok
Jaweria
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can we work on this together little bit ?
Jaweria
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If you dont mind?
dave0616
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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
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can you first show me how to get the value for the 1st rectangle?
dave0616
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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?
dave0616
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@Jaweria
Jaweria
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hand
Jaweria
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we are not allow to use calculator
dave0616
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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
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ok so first I m using 1 for my y
dave0616
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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
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oh ok
dave0616
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so solve for y, using those six values and let me know what you get
Jaweria
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so let me get their values then I ll tell you
Jaweria
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alright
dave0616
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ok, and solve for 1,2,3,4,5 that will give us 5 rectangles
dave0616
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did you get the values?
Jaweria
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so far I got 10,4,0
dave0616
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hmmmm, that first one isnt correct
try it again
Jaweria
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ok
Jaweria
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its 0
dave0616
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that is correct, now go ahead and fine the y value for 4 and 5
Jaweria
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ok
dave0616
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did you solve for them? sorry if i am rushing you, i dont mean to be
dave0616
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@jaweria
Jaweria
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I m sorry my stupid laptop is giving me tough time
dave0616
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its all good no worries
Jaweria
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I got -10
Jaweria
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is that right?
dave0616
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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
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I got -6 for 4
Jaweria
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and -8 for 5
dave0616
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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.
dave0616
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so A=0+4+0-6-8. what do you get for area?
Jaweria
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yeah i got that too all of them
Jaweria
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but then how am i suppose to find an area
add them up?
Jaweria
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and then divide it by some number?
dave0616
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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)
dave0616
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can you solve for area from that?
Jaweria
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oh ok
dave0616
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what do you get for area?
Jaweria
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yeah its -10
Jaweria
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I m still getting -10
dave0616
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thta is right. is that what you were reffering to earlier when you said -10?
Jaweria
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yup
dave0616
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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
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its ok :)
Jaweria
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so thats my answer ?
dave0616
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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
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yup I completely did thanks a lot:)
dave0616
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absolutely no problem!
Jaweria
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I should go to sleep now its really late take care bye.
dave0616
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i hear ya haha. take care and good luck in your studies