integral from 1 to x of (2.25)/(x^3)

解

\int_{1}^{x} \frac{2.25}{x ^{3}} d x

2.25 (- \frac{0.5}{x ^{2}} + 0.5)

解答ステップ

\int_{1}^{x} \frac{2.25}{x ^{3}} d x

定数を除く:

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

= 2.25 \cdot \int_{1}^{x} \frac{1}{x ^{3}} d x

べき乗則を適用する

= 2.25 [- \frac{1}{2 x ^{2}}]_{1}^{x}

簡素化

= 2.25 [- \frac{0.5}{x ^{2}}]_{1}^{x}

限度を計算する:

- \frac{0.5}{x ^{2}} + 0.5

= 2.25 (- \frac{0.5}{x ^{2}} + 0.5)