integral from 1 to cos(x) of 11t^{10}

Lösung

\int_{1}^{c o s (x)} 11 t^{10} d t

cos^{11} (x) - 1

Schritte zur Lösung

\int_{1}^{c o s (x)} 11 t^{10} d t

Entferne die Konstante:

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

= 11 \cdot \int_{1}^{c o s (x)} t^{10} d t

Wende die Potenzregel an

= 11 [\frac{t ^{11}}{11}]_{1}^{c o s (x)}

Berechne die Grenzen:

\frac{cos ^{11} ( x )}{11} - \frac{1}{11}

= 11 (\frac{cos ^{11} ( x )}{11} - \frac{1}{11})

Vereinfache

= cos^{11} (x) - 1

\int_{0}^{y} sin (x) d x

\int_{0}^{1} cos (π) t d t

\int_{- 1}^{2} x + ∣ x ∣ d x

\int_{- π}^{0} (x + π) cos (n x) d x

\int_{0}^{\frac{x}{2}} \frac{sin ( x )}{x} d x