integral from 1 to 3 of ln(x)+sin(x)+8

解

\int_{1}^{3} ln (x) + sin (x) + 8 d x

3 ln (3) + 14 + cos (1) - cos (3)

十進法表記

18.82613 \dots

解答ステップ

\int_{1}^{3} ln (x) + sin (x) + 8 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} ln (x) d x + \int_{1}^{3} sin (x) d x + \int_{1}^{3} 8 d x

\int_{1}^{3} ln (x) d x = 3 ln (3) - 2

\int_{1}^{3} sin (x) d x = - cos (3) + cos (1)

\int_{1}^{3} 8 d x = 16

= 3 ln (3) - 2 - cos (3) + cos (1) + 16

簡素化

= 3 ln (3) + 14 + cos (1) - cos (3)