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anonymous
 one year ago
Write the Riemann sum to find the area under the graph of the function f(x) = x4 from x = 5 to x = 7.
anonymous
 one year ago
Write the Riemann sum to find the area under the graph of the function f(x) = x4 from x = 5 to x = 7.

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441763773280:dw Hint: \[\Large \text{area under f(x) from a to b} = \lim_{n \to \infty} \sum_{i=1}^{n}f(x_i)*\Delta x\] where \[\Large \Delta x =\frac{ba}{n}\] \[\Large x_i = a+i*\Delta x\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I went ahead and did this and got it wrong. Ended up with another one. So can you solve this one as an example @jim_thompson5910

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if a = 5 and b = 7, what is delta x equal to?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wouldn't it equal 0? b is 7, a is 5, and n is infinity?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1ba = 75 = 2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large \Delta x =\frac{ba}{n}\] \[\Large \Delta x =\frac{75}{n}\] \[\Large \Delta x =\frac{2}{n}\] we just leave n as it is

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohhhhhh Makes much more sense

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So how would you finish it off?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what would xi be ?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large x_i = a+i*\Delta x\] \[\Large x_i = ???\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[5+\frac{ 2 }{ n }i ?\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yep or \[\Large 5 + \frac{2i}{n}\] the two are equivalent

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1A = exact area under the curve from x = 5 to x = 7 \[\Large A = \lim_{n \to \infty} \sum_{i=1}^{n}f(x_i)*\Delta x\] \[\Large A = \lim_{n \to \infty} \sum_{i=1}^{n}f\left(5+\frac{2i}{n}\right)*\frac{2}{n}\] \[\Large A = \lim_{n \to \infty} \sum_{i=1}^{n}\left(5+\frac{2i}{n}\right)^4*\frac{2}{n}\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1where \[\Large f(x) = x^4\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So that's the final answer?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Last question, why'd you put the limit there?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1well what the summation does is add up the rectangles (n of them) as you let n approach infinity, the rectangles get smaller and smaller like you see in this animation http://gimyuen.com/wpcontent/uploads/2013/12/riemann_integral.gif

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so as n > infinity, the approximate area gets closer and closer to the true exact area

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OK, I have two similar to this, can I ask you to check over my work?
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