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

- christinestutes

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- pooja195

@Michele_Laino

- christinestutes

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- christinestutes

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## More answers

- melstutes

I have no idea how to do this?

- Michele_Laino

I'm sorry I don't know thta method. Please wait i ask to anothe helper:
@thomaster please help

- Michele_Laino

that*

- Michele_Laino

@IrishBoy123 please help

- 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

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

@mathmath333 please help

- 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

Thank you mathmath

- melstutes

Can anyone help solve a different way?

- 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

there may be way by calculus @Michele_Laino might know, idk much calculus

- melstutes

I am stumped and don't know where to begin.

- Nnesha

graph?http://prntscr.com/7hck7x

- 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

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

|dw:1434398306026:dw|

- 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

Wow, mind blown! I would have NEVER figured that out!

- 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

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

which is close to 10.3

- 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

:)

- IrishBoy123

https://en.wikipedia.org/wiki/Numerical_integration
so " quadrature" = numerical integration

- 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

Feel free to skim through chapter 4, there's plenty of information on quadratures.
http://ins.sjtu.edu.cn/people/mtang/textbook.pdf

- 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

its d

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