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Beliebt Rechnen >

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

Lösung

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

Lösung

8 (3 + \frac{1}{2} ln (2 + 3))

+1

Dezimale

19.12423 \dots

Schritte zur Lösung

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

Wende integrale Reduktion an

= 8 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{3}} + \frac{1}{2} \cdot \int_{0}^{\frac{π}{3}} sec (x) d x)

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

= 8 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{3}} + \frac{1}{2} ln (2 + 3))

Vereinfache

8 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{3}} + \frac{1}{2} ln (2 + 3)) : 8 ([\frac{1}{2} sec (x) tan (x)]_{0}^{\frac{π}{3}} + \frac{1}{2} ln (2 + 3))

= 8 ([\frac{1}{2} sec (x) tan (x)]_{0}^{\frac{π}{3}} + \frac{1}{2} ln (2 + 3))

Berechne die Grenzen:

3

= 8 (3 + \frac{1}{2} ln (2 + 3))

Graph

Beliebte Beispiele

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(\partial)/(\partial x)(ln(x+t^2))

\frac{\partial}{\partial x} (ln (x + t^{2}))

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\int_{- 2}^{- 1} x f (x^{2} + 1) d x