integral from 0 to pi of 2pi(sin(x))

Lösung

\int_{0}^{π} 2 π (sin (x)) d x

4 π

Dezimale

12.56637 \dots

Schritte zur Lösung

\int_{0}^{π} 2 π sin (x) d x

Entferne die Konstante:

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

= 2 π \cdot \int_{0}^{π} sin (x) d x

Nutze das gemeinsame Integral :

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

= 2 π [- cos (x)]_{0}^{π}

Berechne die Grenzen:

2

= 2 π 2

Vereinfache

= 4 π

\int_{y}^{y + 1} 2 y d y

\int_{0}^{12} x (\frac{1}{72} x) d x

\int_{1}^{7} 6 x^{2} + 2 x - 3 d x

\int_{0}^{2} 1 - 0.5 x d x

\int_{0}^{3} \frac{- 2}{5 x + 1} d x