integral from 0 to pi/2 of sin(sqrt(2y))

Lösung

\int_{0}^{\frac{π}{2}} sin (2 y) d y

sin (π) - π cos (π)

Dezimale

1.33474 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} sin (2 y) d y

Wende U-Substitution an

= \int_{0}^{π} u sin (u) d u

Wende die partielle Integration an

= [- u cos (u) - \int - cos (u) d u]_{0}^{π}

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

= [- u cos (u) - (- sin (u))]_{0}^{π}

Vereinfache

= [- u cos (u) + sin (u)]_{0}^{π}

Berechne die Grenzen:

sin (π) - π cos (π)

= sin (π) - π cos (π)