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Beliebt Rechnen >

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

Lösung

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

Lösung

2 (ln (1 + 2) + 2)

+1

Dezimale

4.59117 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende integrale Reduktion an

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

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

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

Vereinfache

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

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

Berechne die Grenzen:

\frac{1}{2}

= 4 (\frac{1}{2} + \frac{1}{2} ln (1 + 2))

Vereinfache

= 2 (ln (1 + 2) + 2)

Graph

Beliebte Beispiele

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