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Math Help - Trapezoidal Rule with uneven subintervals

  1. #1
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    Trapezoidal Rule with uneven subintervals

    This is given:
    f(1)= 2
    f(5)= 10
    f(8)= 13
    f(12)= 17

    Use trapezoidal approximation to find the area of the curve described by the function values above.


    I understand that I need to find the area of all the trapezoids manually. I cannot apply the normal rule because the subintervals are different.

    I used the height as the difference between 1 and 5 and the bases as 2 and 10, whcih plugged into the formula for the area of a trapezoid is \frac{1}{2}( 2 + 10).

    I followed this pattern but my answer was clearly off. It was WAY too big.

    So...how do I solve this problem?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Truthbetold View Post
    This is given:
    f(1)= 2
    f(5)= 10
    f(8)= 13
    f(12)= 17

    Use trapezoidal approximation to find the area of the curve described by the function values above.


    I understand that I need to find the area of all the trapezoids manually. I cannot apply the normal rule because the subintervals are different.

    I used the height as the difference between 1 and 5 and the bases as 2 and 10, whcih plugged into the formula for the area of a trapezoid is \frac{1}{2}( 2 + 10).

    I followed this pattern but my answer was clearly off. It was WAY too big.

    So...how do I solve this problem?

    Using trapesoid rule area from 1 to 5 is 4 \times \frac{2+10}{2}=24.

    area from 5 to 8 is 3 \times \frac{10+13}{2}=34.5

    area from 8 to 12 is 4 \times \frac{13+17}{2}=60.

    RonL
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