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

Lösung

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

1 - \frac{π}{4}

Dezimale

0.21460 \dots

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Multipliziere aus

\frac{1 - cos ^{2} ( x )}{cos ^{2} ( x )} : \frac{1}{cos ^{2} ( x )} - 1

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

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

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

= 1 - \frac{π}{4}

\int_{0}^{3} x^{2} sin (\frac{nπ x}{3}) d x

\int_{0}^{2} (2 x^{2} - 3) d x

\int_{0}^{x^{2}} \frac{1}{x + y} d y

\int_{2}^{6} 8 x d x

\int_{0}^{1} 2 x \cdot e^{x^{2}} d x