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

Lösung

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

2

Dezimale

1.41421 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{\frac{π}{4}} cos (u) \cdot 2 d u

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{\frac{π}{4}} cos (u) d u

Nutze das gemeinsame Integral :

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

= 2 [sin (u)]_{0}^{\frac{π}{4}}

Berechne die Grenzen:

\frac{1}{2}

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

Vereinfache

= 2

\int_{0}^{4} (5 x^{2} - 6 x + 2) d x

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

\int_{1}^{3} (2) d x

\int_{3}^{4} \frac{8}{x ^{2}} d x

\int_{\frac{π}{2}}^{π} (1 + cos (θ))^{2} d θ