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

Lösung

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

cos^{8} (x) - 1

Schritte zur Lösung

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

Entferne die Konstante:

\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

Wende die Potenzregel an

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

Berechne die Grenzen:

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

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

Vereinfache

= cos^{8} (x) - 1

\int_{1}^{2} - \frac{6}{x ^{2}} d x

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