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christinestutes
 one year ago
Use the method of quadrature to estimate the area under the curve and above the xaxis from x = 0 to x = 3.
a. 6.3 c. 20.5
b. 10.3 d. 5
christinestutes
 one year ago
Use the method of quadrature to estimate the area under the curve and above the xaxis from x = 0 to x = 3. a. 6.3 c. 20.5 b. 10.3 d. 5

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melstutes
 one year ago
Best ResponseYou've already chosen the best response.0I have no idea how to do this?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.5I'm sorry I don't know thta method. Please wait i ask to anothe helper: @thomaster please help

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.5@IrishBoy123 please help

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1"method of quadrature" i looked that up earlier and Wiki describes it as an old/ancient term for what we now call Rieman (sp?) sums. so i guess this is precalc numerical solutions for the area under a curve. @melstutes? is that what you are trying to learn?!

melstutes
 one year ago
Best ResponseYou've already chosen the best response.0This is a math essentials class. It is a virtual class that is supposed to be an introductory class. I have never had geometry so I am lost with this.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.5@mathmath333 please help

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1here are some resources i found that might be helpful https://answers.yahoo.com/question/index?qid=20080812222351AAjiurc https://en.wikipedia.org/wiki/Quadrature_(mathematics)

melstutes
 one year ago
Best ResponseYou've already chosen the best response.0Can anyone help solve a different way?

melstutes
 one year ago
Best ResponseYou've already chosen the best response.0This is the definition from the class quadrature  The area of an enclosed region on a plane that can be approximated by the sum of the areas of a number of rectangles.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1there may be way by calculus @Michele_Laino might know, idk much calculus

melstutes
 one year ago
Best ResponseYou've already chosen the best response.0I am stumped and don't know where to begin.

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.0graph? http://prntscr.com/7hck7x

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.5I can try to solve using the rectangles approximation method, nevertheless I'm not sure that it is the requested method

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.5ok! we have to divide the interval into for example three subintervals, as below: \[\begin{gathered} {x_0} = 0, \hfill \\ {x_1} = 1 \hfill \\ {x_2} = 2 \hfill \\ {x_3} = 3 \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.5dw:1434398306026:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.5the requested value is given by the subsequent formula: \[I = \frac{{3  0}}{3}\left( {f\left( 0 \right) + f\left( 1 \right) + f\left( 2 \right)} \right)\]

melstutes
 one year ago
Best ResponseYou've already chosen the best response.0Wow, mind blown! I would have NEVER figured that out!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.5now we have: \[\begin{gathered} f\left( 0 \right) = 5 \hfill \\ f\left( 1 \right) =  \frac{1}{2} + 5 = \frac{9}{2} \hfill \\ f\left( 2 \right) =  \frac{4}{2} + 5 = 3 \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.5so, after a substitution, we get: \[\begin{gathered} I = \frac{{3  0}}{3}\left( {f\left( 0 \right) + f\left( 1 \right) + f\left( 2 \right)} \right) = \hfill \\ \hfill \\ = 5 + \frac{9}{2} + 3 = \frac{{25}}{2} = 12.5 \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.5which is close to 10.3

melstutes
 one year ago
Best ResponseYou've already chosen the best response.0Wow. thank you so much for ALL of your time and explanations. I will need to review what you have done and try more examples.

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1https://en.wikipedia.org/wiki/Numerical_integration so " quadrature" = numerical integration

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0More importantly, a quadrature is (typically) a trapezoidal approximation that depends on an interpolation of a given function using a specific set of points and a polynomial basis. A good example is the Gaussian quadrature: https://en.wikipedia.org/?title=Gaussian_quadrature which is used to approximate integrals of the form \(\displaystyle\int_{1}^1f(x)\,dx\) (and can be extended to approximate integrals over \([a,b]\)).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Feel free to skim through chapter 4, there's plenty of information on quadratures. http://ins.sjtu.edu.cn/people/mtang/textbook.pdf

phi
 one year ago
Best ResponseYou've already chosen the best response.0I would count the number of "squares" under the curve. If there is part of a square try to estimate to the nearest 1/2 square. The idea is to get a reasonable estimate of the area (not an exact number)
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