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Beliebt Rechnen >

integral from 0 to pi/3 of tan(x)

Lösung

\int_{0}^{\frac{π}{3}} tan (x) d x

Lösung

ln (2)

+1

Dezimale

0.69314 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{3}} tan (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{0}^{\frac{π}{3}} \frac{sin ( x )}{cos ( x )} d x

Wende U-Substitution an

= \int_{1}^{\frac{1}{2}} - \frac{1}{u} d u

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

= - \int_{\frac{1}{2}}^{1} - \frac{1}{u} d u

Entferne die Konstante:

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

= - (- \int_{\frac{1}{2}}^{1} \frac{1}{u} d u)

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- [ln ∣ u ∣]_{\frac{1}{2}}^{1})

Vereinfache

= [ln ∣ u ∣]_{\frac{1}{2}}^{1}

Berechne die Grenzen:

ln (2)

= ln (2)

Graph

Beliebte Beispiele

integral from-2 to 2 of |x^2-1|

\int_{- 2}^{2} x^{2} - 1 d x

integral of 4xsqrt(x^2+2x)

\int 4 x x^{2} + 2 x d x

derivative of ln(3x^2+2x-1)

\frac{d}{d x} (ln (3 x^{2} + 2 x - 1))

derivative y=sin^5(2x+1)

d er i v a t i v e y = sin^{5} (2 x + 1)

derivative f(x)=-csc(x)-sin(x)

d er i v a t i v e f (x) = - csc (x) - sin (x)