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Math Help - Integration - Trapazoidal Rule

  1. #1
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    Integration - Trapazoidal Rule

    Hi im stuck on 3 questions from my maths txt book.

    questions 7,11, and 12



    answers are

    7: 0.41
    11: 0.94
    12: 0.92

    my answer for 7 comes up as 5.75, 11 and 12 are off aswell.
    thx in advance all help is appreciated.
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  2. #2
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    Quote Originally Posted by KavX View Post
    Hi im stuck on 3 questions from my maths txt book.

    questions 7,11, and 12

    answers are

    7: 0.41
    11: 0.94
    12: 0.92

    my answer for 7 comes up as 5.75, 11 and 12 are off aswell.
    thx in advance all help is appreciated.
    I'll show you how to do #7. The following questions can be done by the same method:

    \int_0^2 \left(\frac1{x+4}\right) dx is to be approximated by 2 stripes:

    1. Divide the interval [0, 2] into 2 equal parts: [0, 1], (1, 2]. The length of each part is 1.

    2. Calculate
    f(0) = \frac14
    f(1) = \frac15
    f(2) = \frac16

    3. Calculate the area of the 2 trapezoids:
    <br />
\frac{\frac14 + \frac15}{2} \cdot 1 + <br />
\frac{\frac15 + \frac16}{2} \cdot 1 = \frac18 + \frac15 + \frac1{12} = \frac{49}{120} \approx 0.4083... Since the upper border of the trapezoids is allways above the curve this value must be slightly too large.

    4. The exact value is

    \int_0^2 \left(\frac1{x+4}\right) dx = \left. \ln(x+4) \right|_0^2 = \ln(6) - \ln(4) = \ln\left(\frac32\right) \approx 0.405...
    Attached Thumbnails Attached Thumbnails Integration - Trapazoidal Rule-trapezmeth1.jpg  
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  3. #3
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    sweet thx , these are just a breeze now
    i needed to check were im rushing figured out 11. working on 12 now

    F(1)=1
    F(2)=1/4
    F(3)=1/9
    F(4)=1/16
    F(5)=1/25

    h=5-1/4 = 1

    1/2((1+1/25)+2(1/4 +1/9+1/16))

    = 0.9436....

    thx alot they dont seem much of a challenge now.
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