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Math Help - approximate integral

  1. #1
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    Unhappy Help needed!

    I really need some help answering the following question. There is an example of how it should be completed but I don't understand it. The example has a diagram and advises the use of either Trapezium rule or Simpson's rule.

    Question: Use a numerical method to find the area enclosed by the graph of y = x sin x, the x axis and the lines x = 1 and x = 2.
    Use an interval of 0.4

    Thank you for your help!
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  2. #2
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    Quote Originally Posted by norivea
    I really need some help answering the following question. There is an example of how it should be completed but I don't understand it. The example has a diagram and advises the use of either Trapezium rule or Simpson's rule.

    Question: Use a numerical method to find the area enclosed by the graph of y = x sin x, the x axis and the lines x = 1 and x = 2.
    Use an interval of 0.4

    Thank you for your help!
    For example use 4 divisions.
    Then,
    \Delta x=\frac{2-1}{4}=.25
    Thus, (by trapezoid rule),
    .5[f(1)+2f(1.25)+2f(1.5)+2f(1.75)+f(2)]\times .25
    You can do the calculations.
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  3. #3
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    So just for further clarification, I have attached my answer to this post. The area is 4.5248 with n=10 by Trapezium Rule. When you increase the n, or decrease the interval h, the area will be approaching to the real value.
    When n=100, the area is 4.5360
    When n=1000, the area is 4.5361

    Is this correct?
    Attached Thumbnails Attached Thumbnails approximate integral-question.jpg  
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  4. #4
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    Quote Originally Posted by norivea
    So just for further clarification, I have attached my answer to this post. The area is 4.5248 with n=10 by Trapezium Rule. When you increase the n, or decrease the interval h, the area will be approaching to the real value.
    When n=100, the area is 4.5360
    When n=1000, the area is 4.5361

    Is this correct?
    What is K in your image file?

    RonL
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  5. #5
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    Hello, norivea,

    according to the image of your reply

    Quote Originally Posted by norivea
    ...
    Question: Use a numerical method to find the area enclosed by the graph of y = x sin x, the x axis and the lines x = 1 and x = 2.
    Use an interval of 0.4...
    the x-value shoul read 2.6 . Then the given interval make some sense.

    I presume that the K in your image means "continueing"?

    Greetings

    EB
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