integral from pi/6 to pi/3 of 2cos(x)

Lösung

\int_{\frac{π}{6}}^{\frac{π}{3}} 2 cos (x) d x

3 - 1

Dezimale

0.73205 \dots

Schritte zur Lösung

\int_{\frac{π}{6}}^{\frac{π}{3}} 2 cos (x) d x

Entferne die Konstante:

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

= 2 \cdot \int_{\frac{π}{6}}^{\frac{π}{3}} cos (x) d x

Nutze das gemeinsame Integral :

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

= 2 [sin (x)]_{\frac{π}{6}}^{\frac{π}{3}}

Berechne die Grenzen:

\frac{3}{2} - \frac{1}{2}

= 2 (\frac{3}{2} - \frac{1}{2})

Vereinfache

= 3 - 1

\int_{0}^{3} x^{3} + 5 d x

\int_{0}^{0.5} \frac{4}{3} (1 - x^{3}) d x

\int_{0}^{x} 2 (x + y) d y

\int_{x}^{1} \frac{32}{9} (x y)^{\frac{1}{3}} d y

\int_{0}^{2} 1 + 4 x + x^{2} d x