integral from 0 to pi/2 of 3sin(t)cos(t)

Lösung

\int_{0}^{\frac{π}{2}} 3 sin (t) cos (t) d t

\frac{3}{2}

Dezimale

1.5

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} 3 sin (t) cos (t) d t

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{\frac{π}{2}} sin (t) cos (t) d t

Wende U-Substitution an

= 3 \cdot \int_{0}^{1} u d u

Wende die Potenzregel an

= 3 [\frac{u ^{2}}{2}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{2}

= 3 \cdot \frac{1}{2}

Vereinfache

= \frac{3}{2}

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