integral from 0 to sqrt(1-y^2 of)(x+y)

Lösung

\int_{0}^{1 - y^{2}} (x + y) d x

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

Schritte zur Lösung

\int_{0}^{1 - y^{2}} x + y d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1 - y^{2}} y d x + \int_{0}^{1 - y^{2}} x d x

\int_{0}^{1 - y^{2}} y d x = y - y^{2} + 1

\int_{0}^{1 - y^{2}} x d x = \frac{- y ^{2} + 1}{2}

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

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