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--- manual:chapter8:numinteg [2021/10/01 05:26]
jojo1973 created
+++ manual:chapter8:numinteg [2021/10/01 12:35] (current)
jojo1973
@@ Line 61: / Line 61: @@
 ----
-==== Example 1: Bound function on closed interval ====
+==== Example 1: Bounded function on closed interval ====
 |  pic  |  $$ \int^{2}_{0} x^{10}e^{\left(4x^{3}-3x^{4}\right)} \,dx $$  | **Input:**\\ <code>16 SETPREC
@@ Line 69: / Line 69: @@
 tol
 NUMINT</code>  ||
-|  :::  |  tol=10<sup>-4</sup>   | **7.258 3**76 114 514 225 ...  |  Δ = -1.9·10<sup>-5</sup>  |
+|  :::  |  tol=10<sup>-4</sup>   | **7.258 3**76 114 514 225 ...  | %%|Δ|%% = 1.9·10<sup>-5</sup>  |
-|  :::  |  tol=10<sup>-8</sup>   | **7.258 395 17**3 115 920 ...  |  Δ = 2.5·10<sup>-9</sup>  |
+|  :::  |  tol=10<sup>-8</sup>   | **7.258 395 17**3 115 920 ...  | %%|Δ|%% = 2.5·10<sup>-9</sup>  |
-|  :::  |  tol=10<sup>-12</sup>  | **7.258 395 170 61**5 141 ...  |  Δ = 8.5·10<sup>-13</sup>  |
+|  :::  |  tol=10<sup>-12</sup>  | **7.258 395 170 61**5 141 ...  | %%|Δ|%% = 8.5·10<sup>-13</sup>  |
-|  :::  |  Exact at the precision shown  | **[[https://www.wolframalpha.com/input/?i=integrate+x%5E10*exp%284*x%5E3-3*x%5E4%29+from+0+to+2+to+16+digits|7.258 395 170 614 291]]** ...  |   Δ ≤ 10<sup>-16</sup>  |
+|  :::  |  tol=10<sup>-16</sup>  | **7.258 395 170 614** 323 ...  | %%|Δ|%% = 3.2·10<sup>-14</sup>  |
+|  :::  |  Truncated at 16 digits  | **[[https://www.wolframalpha.com/input/?i=integrate+x%5E10*exp%284*x%5E3-3*x%5E4%29+from+0+to+2+to+16+digits|7.258 395 170 614 291]]** ...  |    |
 This integral is interesting because the shape of the function in the interval is flat almost everywhere except for a narrow peak which is however captured by the algorithm.