integral from 0 to pi/6 of cos(2t)

Lösung

\int_{0}^{\frac{π}{6}} cos (2 t) d t

\frac{3}{4}

Dezimale

0.43301 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{6}} cos (2 t) d t

Wende U-Substitution an

= \int_{0}^{\frac{π}{3}} cos (u) \frac{1}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{\frac{π}{3}} cos (u) d u

Nutze das gemeinsame Integral :

\int cos (u) d u = sin (u)

= \frac{1}{2} [sin (u)]_{0}^{\frac{π}{3}}

Berechne die Grenzen:

\frac{3}{2}

= \frac{1}{2} \cdot \frac{3}{2}

Vereinfache

= \frac{3}{4}

\int_{2}^{0} c x d x

\int_{0}^{1} \frac{2}{x ^{3}} d x

\int_{0}^{1} - \frac{( x - 1 ) ^{3}}{3} d x

\int_{0}^{1} 2 π (2 - x) (x - x^{2}) d x

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