integral from 0 to pi/2 of 1/2 cos(x)

Lösung

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

\frac{1}{2}

Dezimale

0.5

Schritte zur Lösung

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

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}{2}} cos (x) d x

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

1

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

Vereinfache

= \frac{1}{2}

\int_{- 2}^{1} 3 x + 4 d x

\int_{0}^{2 π} 3 cos^{2} (θ) d θ

\int_{0}^{5} \frac{50}{x + 5} - 5 d x

\int_{0}^{1} \frac{x ^{6}}{3} d x

\int_{1}^{\infty} \frac{2}{3 x + 7} d x