integral from 0 to sin(y) of (y-2y)

Lösung

\int_{0}^{s i n (y)} (y - 2 y) d y

- \frac{1}{2} sin^{2} (y)

Schritte zur Lösung

\int_{0}^{s i n (y)} y - 2 y d y

Vereinfache

= \int_{0}^{s i n (y)} - y d y

Entferne die Konstante:

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

= - \int_{0}^{s i n (y)} y d y

Wende die Potenzregel an

= - [\frac{y ^{2}}{2}]_{0}^{s i n (y)}

Berechne die Grenzen:

\frac{1}{2} sin^{2} (y)

= - \frac{1}{2} sin^{2} (y)

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