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

Lösung

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

\frac{π}{2 2} - ln (1 + 2)

Dezimale

0.22934 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [x sec (x) - \int sec (x) d x]_{0}^{\frac{π}{4}}

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= [x sec (x) - ln ∣ tan (x) + sec (x) ∣]_{0}^{\frac{π}{4}}

Berechne die Grenzen:

\frac{π}{2 2} - ln (1 + 2)

= \frac{π}{2 2} - ln (1 + 2)

\int_{0}^{π} ∣ sin (x) ∣ cos (n x) d x

\int_{0}^{5} \frac{e ^{x}}{10 + e ^{x}} d x

\int_{0}^{2} k x^{3} d x

\int_{2}^{3} (x + 1) (x^{2} + 2 x)^{3} d x

\int_{0}^{1} e^{- s t} (- t) d t