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