integral from (-pi)/4 to pi/4 of tan(x)

Lösung

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

0

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{\frac{- π}{4}}^{\frac{π}{4}} sin (x) sec (x) d x

Wende die partielle Integration an

= [- \int - tan (x) d x - 1]_{- \frac{π}{4}}^{\frac{π}{4}}

\int - tan (x) d x = ln ∣ cos (x) ∣

= [- ln ∣ cos (x) ∣ - 1]_{- \frac{π}{4}}^{\frac{π}{4}}

Berechne die Grenzen:

0

= 0

\int_{2.5}^{3} (- x^{2} + 4) d x

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