integral from 0 to 1 of (x^{11}+11^x)

解

\int_{0}^{1} (x^{11} + 1 1^{x}) d x

\frac{1}{12} + \frac{10}{ln ( 11 )}

十進法表記

4.25365 \dots

解答ステップ

\int_{0}^{1} x^{11} + 1 1^{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^{11} d x + \int_{0}^{1} 1 1^{x} d x

\int_{0}^{1} x^{11} d x = \frac{1}{12}

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

= \frac{1}{12} + \frac{10}{ln ( 11 )}