integral from-pi/6 to pi/6 of 7sec^2(x)

Lösung

\int_{- \frac{π}{6}}^{\frac{π}{6}} 7 sec^{2} (x) d x

\frac{14}{3}

Dezimale

8.08290 \dots

Schritte zur Lösung

\int_{- \frac{π}{6}}^{\frac{π}{6}} 7 sec^{2} (x) d x

Entferne die Konstante:

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

= 7 \cdot \int_{- \frac{π}{6}}^{\frac{π}{6}} sec^{2} (x) d x

Nutze das gemeinsame Integral :

\int sec^{2} (x) d x = tan (x)

= 7 [tan (x)]_{- \frac{π}{6}}^{\frac{π}{6}}

Berechne die Grenzen:

\frac{2}{3}

= 7 \cdot \frac{2}{3}

Vereinfache

= \frac{14}{3}

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

\int_{0}^{1} x (x + 1)^{- 3} d x

\int_{0}^{1} 1 + u^{2} d u

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

\int_{2}^{1} x d x