integral from-pi/3 to 0 of 6sec^3(x)

Lösung

\int_{- \frac{π}{3}}^{0} 6 sec^{3} (x) d x

6 (3 - \frac{1}{2} ln (2 - 3))

Dezimale

14.34317 \dots

Schritte zur Lösung

\int_{- \frac{π}{3}}^{0} 6 sec^{3} (x) d x

Entferne die Konstante:

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

= 6 \cdot \int_{- \frac{π}{3}}^{0} sec^{3} (x) d x

Wende integrale Reduktion an

= 6 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{- \frac{π}{3}}^{0} + \frac{1}{2} \cdot \int_{- \frac{π}{3}}^{0} sec (x) d x)

\int_{- \frac{π}{3}}^{0} sec (x) d x = - ln (2 - 3)

= 6 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{- \frac{π}{3}}^{0} + \frac{1}{2} (- ln (2 - 3)))

Vereinfache

6 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{- \frac{π}{3}}^{0} + \frac{1}{2} (- ln (2 - 3))) : 6 ([\frac{1}{2} sec (x) tan (x)]_{- \frac{π}{3}}^{0} - \frac{1}{2} ln (2 - 3))

= 6 ([\frac{1}{2} sec (x) tan (x)]_{- \frac{π}{3}}^{0} - \frac{1}{2} ln (2 - 3))

Berechne die Grenzen:

3

= 6 (3 - \frac{1}{2} ln (2 - 3))

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