簡約 (pi+2)/2 ln(pi/4)

解

簡約

\frac{π + 2}{2} ln (\frac{π}{4})

\frac{π + 2}{2} ln (π) - π ln (2) - 2 ln (2)

十進法表記

- 0.62101 \dots

解答ステップ

\frac{π + 2}{2} ln (\frac{π}{4})

対数の規則を適用する:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{π}{4}) = ln (π) - ln (4)

= \frac{π + 2}{2} (ln (π) - ln (4))

ln (4) = 2 ln (2)

= \frac{π + 2}{2} (ln (π) - 2 ln (2))

拡張

\frac{π + 2}{2} (ln (π) - 2 ln (2)) : \frac{π + 2}{2} ln (π) - ln (2) (π + 2)

= \frac{π + 2}{2} ln (π) - ln (2) (π + 2)

拡張

- ln (2) (π + 2) : - π ln (2) - 2 ln (2)

= \frac{π + 2}{2} ln (π) - π ln (2) - 2 ln (2)