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Beliebt Rechnen >

integral from-pi/4 to 0 of 8sec^3(x)

Lösung

\int_{- \frac{π}{4}}^{0} 8 sec^{3} (x) d x

Lösung

4 (- ln (2 - 1) + 2)

+1

Dezimale

9.18234 \dots

Schritte zur Lösung

\int_{- \frac{π}{4}}^{0} 8 sec^{3} (x) d x

Entferne die Konstante:

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

= 8 \cdot \int_{- \frac{π}{4}}^{0} sec^{3} (x) d x

Wende integrale Reduktion an

= 8 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{- \frac{π}{4}}^{0} + \frac{1}{2} \cdot \int_{- \frac{π}{4}}^{0} sec (x) d x)

\int_{- \frac{π}{4}}^{0} sec (x) d x = - ln (2 - 1)

= 8 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{- \frac{π}{4}}^{0} + \frac{1}{2} (- ln (2 - 1)))

Vereinfache

8 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{- \frac{π}{4}}^{0} + \frac{1}{2} (- ln (2 - 1))) : 8 ([\frac{1}{2} sec (x) tan (x)]_{- \frac{π}{4}}^{0} - \frac{1}{2} ln (2 - 1))

= 8 ([\frac{1}{2} sec (x) tan (x)]_{- \frac{π}{4}}^{0} - \frac{1}{2} ln (2 - 1))

Berechne die Grenzen:

\frac{1}{2}

= 8 (\frac{1}{2} - \frac{1}{2} ln (2 - 1))

Vereinfache

= 4 (- ln (2 - 1) + 2)

Graph

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