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Beliebt Rechnen >

integral from 0 to pi/4 of 2tan^4(x)

Lösung

\int_{0}^{\frac{π}{4}} 2 tan^{4} (x) d x

Lösung

2 (- \frac{2}{3} + \frac{π}{4})

+1

Dezimale

0.23746 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} 2 tan^{4} (x) d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{\frac{π}{4}} tan^{4} (x) d x

Wende integrale Reduktion an

= 2 ([\frac{tan ^{3} ( x )}{3}]_{0}^{\frac{π}{4}} - \int_{0}^{\frac{π}{4}} tan^{2} (x) d x)

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

= 2 ([\frac{tan ^{3} ( x )}{3}]_{0}^{\frac{π}{4}} - (- \frac{π}{4} + 1))

Vereinfache

2 ([\frac{tan ^{3} ( x )}{3}]_{0}^{\frac{π}{4}} - (- \frac{π}{4} + 1)) : 2 ([\frac{1}{3} tan^{3} (x)]_{0}^{\frac{π}{4}} + \frac{π}{4} - 1)

= 2 ([\frac{1}{3} tan^{3} (x)]_{0}^{\frac{π}{4}} + \frac{π}{4} - 1)

Berechne die Grenzen:

\frac{1}{3}

= 2 (\frac{1}{3} + \frac{π}{4} - 1)

Vereinfache

= 2 (- \frac{2}{3} + \frac{π}{4})

Graph

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