integral from 1 to cos(x) of 13t^{12}

解

\int_{1}^{c o s (x)} 13 t^{12} d t

cos^{13} (x) - 1

解答ステップ

\int_{1}^{c o s (x)} 13 t^{12} d t

定数を除く:

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

= 13 \cdot \int_{1}^{c o s (x)} t^{12} d t

べき乗則を適用する

= 13 [\frac{t ^{13}}{13}]_{1}^{c o s (x)}

限度を計算する:

\frac{cos ^{13} ( x )}{13} - \frac{1}{13}

= 13 (\frac{cos ^{13} ( x )}{13} - \frac{1}{13})

簡素化

= cos^{13} (x) - 1