integral from 0 to 1 of sin(xy)

Lösung

\int_{0}^{1} sin (x y)

\frac{- cos ( y ) + 1}{y}

Schritte zur Lösung

\int_{0}^{1} sin (x y) d x

Wende U-Substitution an

= \int_{0}^{y} \frac{sin ( u )}{y} d u

Entferne die Konstante:

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

= \frac{1}{y} \cdot \int_{0}^{y} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{y} [- cos (u)]_{0}^{y}

Berechne die Grenzen:

- cos (y) + 1

= \frac{1}{y} (- cos (y) + 1)

Vereinfache

= \frac{- cos ( y ) + 1}{y}

\int_{0}^{1} (10 e^{2 t} - 7) d t

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\int_{4}^{b} x^{5} d x