integral from 1 to sin(x) of 7x^6

Lösung

\int_{1}^{s i n (x)} 7 x^{6} d x

sin^{7} (x) - 1

Schritte zur Lösung

\int_{1}^{s i n (x)} 7 x^{6} d x

Entferne die Konstante:

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

= 7 \cdot \int_{1}^{s i n (x)} x^{6} d x

Wende die Potenzregel an

= 7 [\frac{x ^{7}}{7}]_{1}^{s i n (x)}

Berechne die Grenzen:

\frac{sin ^{7} ( x )}{7} - \frac{1}{7}

= 7 (\frac{sin ^{7} ( x )}{7} - \frac{1}{7})

Vereinfache

= sin^{7} (x) - 1

\int_{0}^{1} y e^{- y} d y

\int_{0}^{1} - 3 x^{2} - 1 d x

\int_{1}^{16} \frac{1}{2 v} d v

\int_{0}^{1} (7 x^{2} - 8 x + 9) d x

\int_{0}^{2 π} (sin (θ))^{2} d θ