Tips for Successful Integration Calculations
When a periodic function or integration interval results in positive and negative f(x) function values
Perform separate integrations for each cycle, or for the positive part and the negative part, and then combine the results.
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When integration values fluctuate widely due to minute shifts in the integration interval
Divide the integration interval into multiple parts (in a way that breaks areas of wide fluctuation into small parts), perform integration on each part, and then combine the results.
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x2
x1 f(x)dx + .....
Examples
1 | sin 30°= 0.5 | 1B | Q30 | 0.5 | |
| sin−10.5 = 30° | 1B | Q(sin−1) 0.5 | 30 | |
2 | sinh 1 = 1.175201194 | @@(sinh) 1 | 1.175201194 | ||
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| @D(cosh−1) 1 | 0 | ||
3 | ΠΠ/2 radians = 90°, 50 grads = 45° B |
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(Π)2 (DRG)A(r) 50 (DRG)B(g)
4 To calculate e5 σ 2 to three significant digits (Sci 3) (SETUP)(Sci)
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| 2() 5 C 2 | 2.97×102 | |
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| 1 | 2() 5 2 | 2.97×102 |
| 5 | log101000 = log 1000 = 3 | 51000 | 3 |
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| log216 = 4 | 52 (,) 16 | 4 |
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| 2 C16 | 4 | |
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| 6 | To calculate ln 90 (= loge 90) to three significant digits (Sci 3) | ||
(SETUP)(Sci) | 290 | 4.50×100 | ||
7 | 1.2 σσ103 = 1200 | 1.2 10 3 | 1200 | |
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| (1+1)2+2 = 16 1 1 2 2 | 16 | |
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| (52)3 = 15625 | 5 V7(x3) | 15625 |
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| 5 32 = 2 () 5 C32 | 2 | |
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| 1 5() 32 | 2 | |
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