integral from 2-y to-y^2+2 of 1/2 y

Lösung

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

\frac{y ^{4} - 5 y ^{2} + 4 y}{4}

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{2 - y}^{- y^{2} + 2} y d y

Wende die Potenzregel an

= \frac{1}{2} [\frac{y ^{2}}{2}]_{2 - y}^{- y^{2} + 2}

Berechne die Grenzen:

\frac{( - y ^{2} + 2 ) ^{2}}{2} - \frac{( 2 - y ) ^{2}}{2}

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

Vereinfache

= \frac{y ^{4} - 5 y ^{2} + 4 y}{4}

\int_{1}^{4} 25 - 5 x d x

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