anonymous
  • anonymous
Evaluate the Riemann sum for (x) = x3 − 6x, for 0 ≤ x ≤ 3 with six subintervals, taking the sample points, xi, to be the right endpoint of each interval. Give three decimal places in your answer.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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freckles
  • freckles
divide 3-0 by 6 to figure out what the length of each sub-interval should be and just take the right endpoint of each sub-interval...
freckles
  • freckles
then once you have the right endpoint of each sub-interval you can find the area of your 6 rectangles and add them up together
anonymous
  • anonymous
So basically I have an interval every half?

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freckles
  • freckles
yes example interval 1 would be [0,1/2] example 2 interval 2 would be [1/2,1] and so on... the right endpoints are 1/2,1,...
freckles
  • freckles
each sub-interval has length 1/2
freckles
  • freckles
so what would be the 3rd sub-interval?
anonymous
  • anonymous
1.5 no?
freckles
  • freckles
do you mean [1,1.5] because a number by itself is not an interval
freckles
  • freckles
and the right endpoint of that interval is 1.5
anonymous
  • anonymous
Yeah sorry.
freckles
  • freckles
[0,1/2] [1/2,1] [1,3/2] [3/2,2] [2,5/2] [5/2,3] these are your 6 subinterval
freckles
  • freckles
you will consider the y values for each right endpoint of each of the sub-intervals
freckles
  • freckles
base of each rectangle is 1/2 you have to evaluate: \[\frac{1}{2}(f(\frac{1}{2})+f(1)+f(\frac{3}{2})+f(2)+f(\frac{5}{2})+f(3)]\]
freckles
  • freckles
I believed when you typed this "(x) = x3 − 6x" you meant f(x)=x^3-6x
anonymous
  • anonymous
You are right. Let me evaluate that.
anonymous
  • anonymous
Am I supposed to get a negative number?
freckles
  • freckles
that is what I have
freckles
  • freckles
we could get a better idea of why that is by graphing the thingy on [0,3]
anonymous
  • anonymous
Ok, but it is equal to -3.94?
freckles
  • freckles
|dw:1446582332581:dw| it is definitely a net area that area below the x-axis must have been bigger then the area of above the x-axis since we got a negative result and yes -3.94 is what I have too
freckles
  • freckles
|dw:1446582432385:dw|
freckles
  • freckles
according to the rule we us |A1|>|A2| since we were given A1+A2 is negative
anonymous
  • anonymous
Funny thing is my next question was to prove it by graph and you've done just that, really helped me understand it much better than when I asked it last time, thanks. 10/10
freckles
  • freckles
prove it by graph?
freckles
  • freckles
is that what is says?
anonymous
  • anonymous
I'm sorry, explain using a graph.
anonymous
  • anonymous
I'd just divide it up into intervals and then use geometry no?
anonymous
  • anonymous
|dw:1446582923318:dw|
freckles
  • freckles
|dw:1446582835492:dw| yep was just drawing that :P