integral from a to 2a of a-(a^3)/(x^2)

解

\int_{a}^{2 a} a - \frac{a ^{3}}{x ^{2}} d x

a^{2} - \frac{a ^{2}}{2}

解答ステップ

\int_{a}^{2 a} a - \frac{a ^{3}}{x ^{2}} 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_{a}^{2 a} a d x - \int_{a}^{2 a} \frac{a ^{3}}{x ^{2}} d x

\int_{a}^{2 a} a d x = a^{2}

\int_{a}^{2 a} \frac{a ^{3}}{x ^{2}} d x = \frac{a ^{2}}{2}

= a^{2} - \frac{a ^{2}}{2}