integral from pi/4 to pi/3 of tan^2(x)

Lösung

\int_{\frac{π}{4}}^{\frac{π}{3}} tan^{2} (x) d x

- \frac{π}{12} + 3 - 1

Dezimale

0.47025 \dots

Schritte zur Lösung

\int_{\frac{π}{4}}^{\frac{π}{3}} tan^{2} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{\frac{π}{4}}^{\frac{π}{3}} - 1 + sec^{2} (x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{\frac{π}{4}}^{\frac{π}{3}} 1 d x + \int_{\frac{π}{4}}^{\frac{π}{3}} sec^{2} (x) d x

\int_{\frac{π}{4}}^{\frac{π}{3}} 1 d x = \frac{π}{12}

\int_{\frac{π}{4}}^{\frac{π}{3}} sec^{2} (x) d x = 3 - 1

= - \frac{π}{12} + 3 - 1

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