christinestutes
  • christinestutes
Use the method of quadrature to estimate the area under the curve and above the x-axis from x = 0 to x = 3. a. 6.3 c. 20.5 b. 10.3 d. 5
Geometry
schrodinger
  • schrodinger
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pooja195
  • pooja195
christinestutes
  • christinestutes
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christinestutes
  • christinestutes

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melstutes
  • melstutes
I have no idea how to do this?
Michele_Laino
  • Michele_Laino
I'm sorry I don't know thta method. Please wait i ask to anothe helper: @thomaster please help
Michele_Laino
  • Michele_Laino
that*
Michele_Laino
  • Michele_Laino
@IrishBoy123 please help
IrishBoy123
  • IrishBoy123
"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 pre-calc numerical solutions for the area under a curve. @melstutes? is that what you are trying to learn?!
melstutes
  • melstutes
This 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
  • Michele_Laino
@mathmath333 please help
mathmath333
  • mathmath333
here 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
  • melstutes
Thank you mathmath
melstutes
  • melstutes
Can anyone help solve a different way?
melstutes
  • melstutes
This 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
  • mathmath333
there may be way by calculus @Michele_Laino might know, idk much calculus
melstutes
  • melstutes
I am stumped and don't know where to begin.
Nnesha
  • Nnesha
graph?http://prntscr.com/7hck7x
Michele_Laino
  • Michele_Laino
I can try to solve using the rectangles approximation method, nevertheless I'm not sure that it is the requested method
Michele_Laino
  • Michele_Laino
ok! 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
  • Michele_Laino
|dw:1434398306026:dw|
Michele_Laino
  • Michele_Laino
the 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
  • melstutes
Wow, mind blown! I would have NEVER figured that out!
Michele_Laino
  • Michele_Laino
now 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
  • Michele_Laino
so, 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
  • Michele_Laino
which is close to 10.3
melstutes
  • melstutes
Wow. thank you so much for ALL of your time and explanations. I will need to review what you have done and try more examples.
Michele_Laino
  • Michele_Laino
:)
IrishBoy123
  • IrishBoy123
https://en.wikipedia.org/wiki/Numerical_integration so " quadrature" = numerical integration
anonymous
  • anonymous
More 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
  • anonymous
Feel free to skim through chapter 4, there's plenty of information on quadratures. http://ins.sjtu.edu.cn/people/mtang/textbook.pdf
phi
  • phi
I 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)
anonymous
  • anonymous
its d

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