HP 35s Scientific Calculator Manuel d'utilisateur télécharger pdf (Page 339)

100

101

More about Integration E-3

With this number of sample points, the algorithm will calculate the same

approximation for the integral of any of the functions shown. The actual integrals of

the functions shown with solid blue and black lines are about the same, so the

approximation will be fairly accurate if f(x) is one of these functions. However, the

actual integral of the function shown with a dashed line is quite different from those

of the others, so the current approximation will be rather inaccurate if f(x) is this

function.

The algorithm comes to know the general behavior of the function by sampling the

function at more and more points. If a fluctuation of the function in one region is not

unlike the behavior over the rest of the interval of integration, at some iteration the

algorithm will likely detect the fluctuation. When this happens, the number of

sample points is increased until successive iterations yield approximations that take

into account the presence of the most rapid, but characteristic, fluctuations.

For example, consider the approximation of

Since you're evaluating this integral numerically, you might think that you should

represent the upper limit of integration as 10

499

, which is virtually the largest

number you can key into the calculator.

f (x)

∫

∞

−

dxxe

1 2 ... 334 335 336 337 338 339 340 341 342 343 344 ... 381 382

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HP 35s Scientific Calculator Manuel d'utilisateur Page 339

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