integral from 1 to 3 of (9^x-7^x)

解

\int_{1}^{3} (9^{x} - 7^{x}) d x

\frac{360}{ln ( 3 )} - \frac{336}{ln ( 7 )}

十進法表記

155.01627 \dots

解答ステップ

\int_{1}^{3} 9^{x} - 7^{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_{1}^{3} 9^{x} d x - \int_{1}^{3} 7^{x} d x

\int_{1}^{3} 9^{x} d x = \frac{360}{ln ( 3 )}

\int_{1}^{3} 7^{x} d x = \frac{336}{ln ( 7 )}

= \frac{360}{ln ( 3 )} - \frac{336}{ln ( 7 )}