1.
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The graph of f(x) on [0,1] is
by (1)estimating the values for f(x) at x = 0, 0.2,0.4, 0.6, 0.8, 1, (2)inserting them in the table below, (3)and then using these values to estimate the integral by the trapezoidal rule. In making he table, allow yourself an error (in absolute value) of .02 in each entry of the table. In addition state whether the trapezoidal approximation is an overestimate or underestimate of the value of the integral. |
Solution:
Reading the graph, and using the fact that the ticks on the y-axis have a difference .04 we can say that the f values are
|
x |
0 |
.2 |
.4 |
.6 |
.8 |
1 |
|
f(x) |
1 |
.54 |
.36 |
.22. |
.1 |
0 |
To verify that these estimates are correct, with an error of at most .02 consider the value at 0.6. By the graph, it lies between .2 and .24. Thus f(.6) will be .22 with an error of at most
(.24-.20)/2 = 0.02. The same argument applys at the other points.
By the Trapezoidal sum rule, the integral is approximately equal to
.2(1/2 + .54 + .36+.22 + .1 + 0/2)=.2(1.72) = .34
