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Exercises

  1. Approximate \(\int_0^2 f(x) dx\) from the tabulation in the Table below:

    x f(x) 0.00 1.0000 0.12 0.8869 0.53 0.5886 0.87 0.4190 1.08 0.3396 1.43 0.2393 2.00 0.1353

  1. The table below is a tabulation of various values of the hyperbolic cosine function.

    x cosh(x) 1.0 1.54308063481524
    1.1 1.66851855382226
    1.2 1.81065556732437
    1.3 1.97091423032663
    1.4 2.15089846539314
    1.5 2.35240961524325
    1.6 2.57746447119489
    1.7 2.82831545788997
    1.8 3.10747317631727
    2.0 3.76219569108363
    2.2 4.56790832889823
    2.4 5.55694716696551
    2.6 6.76900580660801
    2.8 8.25272841686113
    3.0 10.0676619957778
    3.3 13.5747610440296
    3.6 18.3127790830626
    3.9 24.711345508488
    4.2 33.3506633088728
    4.6 49.7471837388392
    5.0 74.2099485247878
    5.5 122.348009517829
    6.0 201.715636122456
    7.0 548.317035155212
    8.0 1490.47916125218
    9.0 4051.54202549259

Approximate \(\int_1^{9.0} cosh(x) dx\) from the tabulation above.

  1. The table below is a tabulation of various values of the hyperbolic cosine function.

    x cosh(x) 1.0 1.54308063481524
    1.1 1.66851855382226
    1.2 1.81065556732437
    1.3 1.97091423032663
    1.4 2.15089846539314
    1.5 2.35240961524325
    1.6 2.57746447119489
    1.7 2.82831545788997
    1.8 3.10747317631727
    2.0 3.76219569108363
    2.2 4.56790832889823
    2.4 5.55694716696551
    2.6 6.76900580660801
    2.8 8.25272841686113
    3.0 10.0676619957778
    3.3 13.5747610440296
    3.6 18.3127790830626
    3.9 24.711345508488
    4.2 33.3506633088728
    4.6 49.7471837388392
    5.0 74.2099485247878
    5.5 122.348009517829
    6.0 201.715636122456
    7.0 548.317035155212
    8.0 1490.47916125218
    9.0 4051.54202549259

Approximate \(\int_1^{4.2} cosh(x) dx\) from the tabulation above. Briefly explain how you handle starting and stopping the integration from values that are intermediate and are tabulated.

  1. (Advanced) The table below is a tabulation of various values of the hyperbolic cosine function.

    x cosh(x) 1.0 1.54308063481524
    1.1 1.66851855382226
    1.2 1.81065556732437
    1.3 1.97091423032663
    1.4 2.15089846539314
    1.5 2.35240961524325
    1.6 2.57746447119489
    1.7 2.82831545788997
    1.8 3.10747317631727
    2.0 3.76219569108363
    2.2 4.56790832889823
    2.4 5.55694716696551
    2.6 6.76900580660801
    2.8 8.25272841686113
    3.0 10.0676619957778
    3.3 13.5747610440296
    3.6 18.3127790830626
    3.9 24.711345508488
    4.2 33.3506633088728
    4.6 49.7471837388392
    5.0 74.2099485247878
    5.5 122.348009517829
    6.0 201.715636122456
    7.0 548.317035155212
    8.0 1490.47916125218
    9.0 4051.54202549259

Approximate \(\int_1^{4.0} cosh(x) dx\) from the tabulation above. Explain how handled working with values that fall between tabulated values.