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anonymous
 one year ago
Use the right endpoint and 6 rectangles to find the approximation of the area of the region between the x axis and between the interval [2, 5]
f(x) = 2x^2  x 1. I'll post my work so far done.
anonymous
 one year ago
Use the right endpoint and 6 rectangles to find the approximation of the area of the region between the x axis and between the interval [2, 5] f(x) = 2x^2  x 1. I'll post my work so far done.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sum_{i = 1}^{6} f(x)\Delta x\] Delta x is the width of each rectangle which is: \[\frac{ 5  2 }{ 6 } = \frac{ 1 }{ 2 }\] The counter for the right endpoint is: \[i (\frac{ 1 }{ 2 }) = \frac{ i }{ 2 }\] \[\sum_{i = 1}^{6} (2x^2  x  1)(\frac{ 1 }{ 2 })\] since 1/2 is constant it can be in front \[(\frac{ 1 }{ 2 })\sum_{i = 1}^{6} (2x^2  x  1)\] \[(\frac{ 1 }{ 2 }) \sum_{i =1}^{6} 2x^2  \sum_{i =1}^{6} x  \sum_{i =1}^{6} 1\] \[(\frac{ 1 }{ 2 }) \sum_{i =1}^{6} 2(\frac{ i }{ 2 })^2  \sum_{i =1}^{6} (\frac{ i }{ 2 })  \sum_{i =1}^{6} 1\] Is what I did until now correct?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1Something seems off. Let me think

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 I'm supposed to use sigma (summation) notation not the definite integral method I think I should have a parenthesis or bracket around all the sigma notations

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1ok I see what went wrong you start at a = 2 each term xi is defined as xi = a + i*(delta x) so plug in a = 2 and delta x = 0.5 to get xi = a + i*(delta x) xi = 2 + i*(0.5) xi = 2 + 0.5i so you should have \[\Large \sum_{i = 1}^{6} f(x_i)\Delta x\] \[\Large \sum_{i = 1}^{6} f(2+0.5i)0.5\] \[\Large 0.5\sum_{i = 1}^{6}[2x_i^2  x_i  1]\] \[\Large 0.5\sum_{i = 1}^{6}[ 2(2+0.5i)^2(2+0.5i)1]\] hopefully that makes sense

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 Thank you. Looking it over. Didn't digest all of it yet.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think I get it now. Will crunch the numbers.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1tell me what you get

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I didn't realize that xi is: a + i(delta x). The problems we did in class a equaled 0. So now I realize xi for this example is: 2 + i(delta x) so I need to replace each x with 2 + (i/2). Please let me know if I'm still missing something

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1well in this case, a = 2 and b = 5 so maybe what your teacher did was shift all of f(x) 2 units to the left, so that a = 0 is the start of your interval

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Correct. So I was thrown off with this one.
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