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人気のある微分積分 >

integral from 1 to cos(x) of 8t^7

解

\int_{1}^{c o s (x)} 8 t^{7} d t

解

cos^{8} (x) - 1

解答ステップ

\int_{1}^{c o s (x)} 8 t^{7} d t

定数を除く:

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

= 8 \cdot \int_{1}^{c o s (x)} t^{7} d t

べき乗則を適用する

= 8 [\frac{t ^{8}}{8}]_{1}^{c o s (x)}

限度を計算する:

\frac{cos ^{8} ( x )}{8} - \frac{1}{8}

= 8 (\frac{cos ^{8} ( x )}{8} - \frac{1}{8})

簡素化

= cos^{8} (x) - 1

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