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Math Help - Using simpsons rule integration

  1. #1
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    Using simpsons rule integration

    simpsons rule... (please let me know if I've copied this wrong!!)

    w/3 [(y0+yn+4(y1+y3+y5....)+2(y2+y4+y6...)]

    I got my q

    ∫(below)0 (above)2π /3 sin x dx (4 strips)


    can I please have some help??
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  2. #2
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    Quote Originally Posted by hoppingmad View Post
    simpsons rule... (please let me know if I've copied this wrong!!)

    w/3 [(y0+yn+4(y1+y3+y5....)+2(y2+y4+y6...)]

    I got my q

    ∫(below)0 (above)2π /3 sin x dx (4 strips)


    can I please have some help??
    \int_0^{\frac{2\pi}{3}} \sin{x} \, dx = \frac{\pi}{18}\left[\sin(0) + 4\sin\left(\frac{\pi}{6}\right) + 2\sin\left(\frac{\pi}{3}\right) + 4\sin\left(\frac{\pi}{2}\right) + \sin\left(\frac{2\pi}{3}\right)\right]<br />
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  3. #3
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    \int_0^{\frac{2\pi}{3}} \sin{x} \, dx = \frac{\pi}{18}\left[\sin(0) + 4\sin\left(\frac{\pi}{6}\right) + 2\sin\left(\frac{\pi}{3}\right) + 4\sin\left(\frac{\pi}{2}\right) + \sin\left(\frac{2\pi}{3}\right)\right]<br />

    okay see I'm getting...

    \int_0^{\frac{2\pi}{3}} \sin{x} \, dx = pi/18 [sin (0) + sin (120) + 4 (0.5 + 1) + 2(sin 120)]<br />

    which goes as pi/18 [0 + root3/2 + 4(1.5) + root3]

    in which I get the answer as approximate to 1.5

    The answer in the textbook is 3.0

    I'm not sure I completely understand your working skeeter...
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  4. #4
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    Quote Originally Posted by hoppingmad View Post
    \int_0^{\frac{2\pi}{3}} \sin{x} \, dx = \frac{\pi}{18}\left[\sin(0) + 4\sin\left(\frac{\pi}{6}\right) + 2\sin\left(\frac{\pi}{3}\right) + 4\sin\left(\frac{\pi}{2}\right) + \sin\left(\frac{2\pi}{3}\right)\right]<br />

    okay see I'm getting...

    \int_0^{\frac{2\pi}{3}} \sin{x} \, dx = pi/18 [sin (0) + sin (120) + 4 (0.5 + 1) + 2(sin 120)]<br />

    which goes as pi/18 [0 + root3/2 + 4(1.5) + root3]

    in which I get the answer as approximate to 1.5

    The answer in the textbook is 3.0

    I'm not sure I completely understand your working skeeter...
    \frac{\Delta x}{3} \left(y_0 + 4y_1 + 2y_2 + 4y_3 + y_4\right)

    \Delta x = \frac{\pi}{6}

    y_0 = \sin(0)

    y_1 = \sin\left(\frac{\pi}{6}\right)

    y_2 = \sin\left(\frac{\pi}{3}\right)

    y_3 = \sin\left(\frac{\pi}{2}\right)

    y_4 = \sin\left(\frac{2\pi}{3}\right)

    you have the same values as I , except you are mixing degrees with radians. don't do that.

    note that you were lucky since sin(120) = sin(60) ... you listed sin(120) twice.
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  5. #5
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    Quote Originally Posted by skeeter View Post
    \frac{\Delta x}{3} \left(y_0 + 4y_1 + 2y_2 + 4y_3 + y_4\right)

    \Delta x = \frac{\pi}{6}

    y_0 = \sin(0)

    y_1 = \sin\left(\frac{\pi}{6}\right)

    y_2 = \sin\left(\frac{\pi}{3}\right)

    y_3 = \sin\left(\frac{\pi}{2}\right)

    y_4 = \sin\left(\frac{2\pi}{3}\right)

    you have the same values as I , except you are mixing degrees with radians. don't do that.

    note that you were lucky since sin(120) = sin(60) ... you listed sin(120) twice.
    okay... don't mix... makes sense... but if we are still getting the same answers I must have understood something... But I'm still getting 1.5 as the value? Can I ask what are you getting when you type it all in?
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  6. #6
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    Quote Originally Posted by hoppingmad View Post
    okay... don't mix... makes sense... but if we are still getting the same answers I must have understood something... But I'm still getting 1.5 as the value? Can I ask what are you getting when you type it all in?
    1.5 is the exact value of the integral ... you should be getting 1.500647392

    simpson's rule is, after all, an approximation.
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  7. #7
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    Quote Originally Posted by skeeter View Post
    1.5 is the exact value of the integral ... you should be getting 1.500647392

    simpson's rule is, after all, an approximation.
    I'm in highschool we always go to 2 decimal places haha
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