integral from 0 to 1 of tan(x)

Lösung

\int_{0}^{1} tan (x) d x

- ln (cos (1))

Dezimale

0.61562 \dots

Schritte zur Lösung

\int_{0}^{1} tan (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{0}^{1} \frac{sin ( x )}{cos ( x )} d x

Wende U-Substitution an

= \int_{1}^{c o s (1)} - \frac{1}{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{c o s (1)}^{1} - \frac{1}{u} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - (- \int_{c o s (1)}^{1} \frac{1}{u} d u)

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- [ln ∣ u ∣]_{c o s (1)}^{1})

Vereinfache

= [ln ∣ u ∣]_{c o s (1)}^{1}

Berechne die Grenzen:

- ln (cos (1))

= - ln (cos (1))

\int_{x}^{x^{2}} \frac{y}{x} d y

\int_{- 1}^{1} sin (x) d x

\int_{1}^{4} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

\int_{2}^{5} x^{2} + 5 x d x

\int_{- e - 1}^{- 2} \frac{1}{1 + x} d x