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

解答

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

- 11.56789 \dots

求解步骤

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

使用积分加法定则:

\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}

化简

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

= - 11.56789 \dots

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