integral from 0 to 1 of (x^{10}+10^x)

解

\int_{0}^{1} (x^{10} + 1 0^{x}) d x

\frac{1}{11} + \frac{9}{ln ( 10 )}

十進法表記

3.99955 \dots

解答ステップ

\int_{0}^{1} x^{10} + 1 0^{x} d x

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}^{1} x^{10} d x + \int_{0}^{1} 1 0^{x} d x

\int_{0}^{1} x^{10} d x = \frac{1}{11}

\int_{0}^{1} 1 0^{x} d x = \frac{9}{ln ( 10 )}

= \frac{1}{11} + \frac{9}{ln ( 10 )}