integral from 0.5 to 1 of (p^3-e^{4p})

解

\int_{0.5}^{1} (p^{3} - e^{4 p}) d p

- 11.56789 \dots

解答ステップ

\int_{0.5}^{1} p^{3} - e^{4 p} d p

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0.5}^{1} p^{3} d p - \int_{0.5}^{1} e^{4 p} d p

\int_{0.5}^{1} p^{3} d p = 0.234375

\int_{0.5}^{1} e^{4 p} d p = \frac{e ^{4} - e ^{2}}{4}

= 0.234375 - \frac{e ^{4} - e ^{2}}{4}

簡素化

0.234375 - \frac{e ^{4} - e ^{2}}{4} : - 11.56789 \dots

= - 11.56789 \dots