Anonymous
Anonymous asked in Science & MathematicsMathematics · 8 months ago

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.?

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  • david
    Lv 7
    8 months ago

    a. Trap ... (b - a)/n = width of each subinterval

    (3-2)/10 = 0.1

    sub intervals -- (2, 2.1), (2.1,2.2), (2.2,2.3) etc

    area of each trap. = (1/2)[f(left end pt) + f(right end pt)](width)

    1st sub = (1/2)[f(2.0) + f(2.1)](0.1)

    2nd sub = (1/2)[f(2.1) + f(2.2)](0.1)

    3rd sub = (1/2)[f(2.2) + f(2.3)](0.1)

    ..... etc

    10th sub = (1/2)[f(2.9) + f(3.0)](0.1)

    ===========================================

    answer is the sum of all sub intervals

    you can do the rest, just substitute into the function and do the math ...

    good luck.

    ==========================================

    Midpoint rule === same subintervals as above

    midpoint of 1st sub = (2.0 + 2.1)/2

    midpoint of 2nd sub = (2.1 + 2.2)/2

    midpoint of 3rd sub = (2.2 + 2.3)/2

    ..... etc ...

    Area of 1st sub = f(mid pt 1)*(width)

    Area of 2nd sub = f(mid pt 2)*(width)

    .... etc ...

    Answer is sum of all sub areas above

    ... again just substitute and start calculating

    ... Good luck -- and get started it will take some time.

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  • Bryce
    Lv 7
    8 months ago

    a. 2.6441741782

    b. 2.6698605714

    c. 2.6555814043

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