integral from 1 to t of (17)/(x^3)

解

\int_{1}^{t} \frac{17}{x ^{3}} d x

17 (- \frac{1}{2 t ^{2}} + \frac{1}{2})

解答ステップ

\int_{1}^{t} \frac{17}{x ^{3}} d x

定数を除く:

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

= 17 \cdot \int_{1}^{t} \frac{1}{x ^{3}} d x

べき乗則を適用する

= 17 [- \frac{1}{2 x ^{2}}]_{1}^{t}

限度を計算する:

- \frac{1}{2 t ^{2}} + \frac{1}{2}

= 17 (- \frac{1}{2 t ^{2}} + \frac{1}{2})