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

Lösung

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

- \frac{π}{4} + 1

Dezimale

0.21460 \dots

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

\int_{0}^{\frac{π}{4}} 1 d x = \frac{π}{4}

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

= - \frac{π}{4} + 1

\int \frac{3 x ^{2}}{125} d x

d er i v a t i v e sin (cos (tan (x)))

\frac{d}{d x} (1 + cos (2 x))

d er i v a t i v e y = 5 x^{4}

im pl i c i t ln (x y^{9}) = x y