MA2160: Quiz Oct 8th
Name:_______________________

Show your work for full points.

({{      }})   1)Write sums for the following approximations to (∫_2^4)f[x]dx using the values of f in the table.

({{"x", "f[x]"}, {"1.000", "4.84"}, {"1.125", "5.02"}, {"1.250", "5.19"}, {"1.375", "5.35"}, {"1.500", "5.50"}, {"1.625", "5.62"}, {"1.750", "5.72"}, {"1.875", "5.79"}, {"2.000", "5.82"}, {"2.125", "5.81"}, {"2.250", "5.75"}, {"2.375", "5.65"}, {"2.500", "5.50"}, {"2.625", "5.30"}, {"2.750", "5.05"}, {"2.875", "4.76"}, {"3.000", "4.42"}, {"3.125", "4.05"}, {"3.250", "3.65"}, {"3.375", "3.22"}, {"3.500", "2.77"}, {"3.625", "2.32"}, {"3.750", "1.86"}, {"3.875", "1.41"}, {"4.000", "0.97"}})   ({{a) Left Hand Sum with 4 subdivisions.



}, {b) Left Hand Sum with 4 subdivisions.

}, {c) Mid Point with 4 subdivisions.         

     }, {d) Trap Rule with 4 subdivisions.
   
}, {e) Simpsons rule.  



                                            }})

f[x_]= x Sin[x]+ 4;
Grid[
Join[
{{"x","f[x]"}},
Table[
{NumberForm[x,{4,3}],NumberForm[f[x],{3,2}]},
{x,1,4,0.125}]
],
Alignment->{Left},
Dividers->All
]

({{"x", "f[x]"}, {"1.000", "4.84"}, {"1.125", "5.02"}, {"1.250", "5.19"}, {"1.375", "5.35"}, {"1.500", "5.50"}, {"1.625", "5.62"}, {"1.750", "5.72"}, {"1.875", "5.79"}, {"2.000", "5.82"}, {"2.125", "5.81"}, {"2.250", "5.75"}, {"2.375", "5.65"}, {"2.500", "5.50"}, {"2.625", "5.30"}, {"2.750", "5.05"}, {"2.875", "4.76"}, {"3.000", "4.42"}, {"3.125", "4.05"}, {"3.250", "3.65"}, {"3.375", "3.22"}, {"3.500", "2.77"}, {"3.625", "2.32"}, {"3.750", "1.86"}, {"3.875", "1.41"}, {"4.000", "0.97"}})