integral from 1 to cos(x) of 10t^9

解

\int_{1}^{c o s (x)} 10 t^{9} d t

cos^{10} (x) - 1

解答ステップ

\int_{1}^{c o s (x)} 10 t^{9} d t

定数を除く:

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

= 10 \cdot \int_{1}^{c o s (x)} t^{9} d t

べき乗則を適用する

= 10 [\frac{t ^{10}}{10}]_{1}^{c o s (x)}

限度を計算する:

\frac{cos ^{10} ( x )}{10} - \frac{1}{10}

= 10 (\frac{cos ^{10} ( x )}{10} - \frac{1}{10})

簡素化

= cos^{10} (x) - 1