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Math Help - Approximate Integration (trapezoids, midpoint, and simpson's rule)

  1. #1
    Member FalconPUNCH!'s Avatar
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    Approximate Integration (trapezoids, midpoint, and simpson's rule)



    I couldn't get the answer for the trapezoid correct, so I haven't tried the other two rules.

    Here's what I tried:

     \triangle{x} = \frac{\pi}{10}

    I used the trapezoid rule

     T_n = \frac{\triangle{x}}{2} [ f(x_0) + 2f(x_1) + 2f(x_2) + ... + 2f(x_{n-1}) + f(x_n)]

    Here's my work:


    T_n = \frac{\frac{\pi}{10}}{2} [ sin(0) + 2sin(\frac{\pi}{10}) + 2sin(\frac{\pi}{5}) + 2sin(\frac{3\pi}{10}) + 2sin(\frac{\pi}{2.5})  + 2sin(\frac{\pi}{2}) + 2sin(\frac{3\pi}{5}) + 2sin(\frac{7\pi}{10}) + 2sin(\frac{4\pi}{5}) + 2sin(\frac{9\pi}{10}) + sin(\pi)

    I get approximately .086106 as my answer, but the book has the answer to almost 1.9.

    Any idea what I did wrong?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by FalconPUNCH! View Post


    I couldn't get the answer for the trapezoid correct, so I haven't tried the other two rules.

    Here's what I tried:

     \triangle{x} = \frac{\pi}{10}

    I used the trapezoid rule

     T_n = \frac{\triangle{x}}{2} [ f(x_0) + 2f(x_1) + 2f(x_2) + ... + 2f(x_{n-1}) + f(x_n)]

    Here's my work:


    T_n = \frac{\frac{\pi}{10}}{2} [ sin(0) + 2sin(\frac{\pi}{10}) + 2sin(\frac{\pi}{5}) + 2sin(\frac{3\pi}{10}) + 2sin(\frac{\pi}{2.5})  + 2sin(\frac{\pi}{2}) + 2sin(\frac{3\pi}{5}) + 2sin(\frac{7\pi}{10}) + 2sin(\frac{4\pi}{5}) + 2sin(\frac{9\pi}{10}) + sin(\pi)

    I get approximately .086106 as my answer, but the book has the answer to almost 1.9.

    Any idea what I did wrong?
    Check the angle mode on your calculator, it should be radians.

    RonL
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  3. #3
    Member FalconPUNCH!'s Avatar
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    Daly City, CA
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    Quote Originally Posted by CaptainBlack View Post
    Check the angle mode on your calculator, it should be radians.

    RonL
    OMG you're right!! I feel so stupid
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