But since integrating a positive function, take absolute value:
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- ∫ a^u du = u / (ln a), but a = 0.5, ln(0.5) < 0
- So ∫ (0.5)^u du = u / (ln 0.5) = u / (-ln 2) = -u / ln 2
- So ∫₁² (0.5)^u du = [ -u / ln2 ]₁² = ( -2/ln2 ) - ( -1/ln2 ) = -1/ln2
- = 1/ln2 ≈ 1.4427
- Then total = 20k × (1/ln2) = 20 × 636.39 × 1.4427 ≈ 12727.8 × 1.4427 ≈ 18368 — still wrong.
- Alternative: use discrete approximation or reconsider.
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