integral from 1 to 2 of [(inx)/(x^2)]

解

\int_{1}^{2} [\frac{in x}{x ^{2}}] d x

in ln (2)

解答ステップ

\int_{1}^{2} \frac{in x}{x ^{2}} d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= in \cdot \int_{1}^{2} \frac{x}{x ^{2}} d x

共通因数を約分する:

x

= in \cdot \int_{1}^{2} \frac{1}{x} d x

共通積分を使用する:

\int \frac{1}{x} d x = ln (∣ x ∣)

= in [ln ∣ x ∣]_{1}^{2}

限度を計算する:

ln (2)

= in ln (2)