integral from-y to y of c(y^2-x^2)e^{-y}

Lösung

\int_{- y}^{y} c (y^{2} - x^{2}) e^{- y} d x

c e^{- y} (2 y^{3} - \frac{2 y ^{3}}{3})

Schritte zur Lösung

\int_{- y}^{y} c (y^{2} - x^{2}) e^{- y} d x

Entferne die Konstante:

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

= c e^{- y} \cdot \int_{- y}^{y} y^{2} - x^{2} 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

= c e^{- y} (\int_{- y}^{y} y^{2} d x - \int_{- y}^{y} x^{2} d x)

\int_{- y}^{y} y^{2} d x = 2 y^{3}

\int_{- y}^{y} x^{2} d x = \frac{2 y ^{3}}{3}

= c e^{- y} (2 y^{3} - \frac{2 y ^{3}}{3})

\int_{0}^{\frac{5}{11}} \frac{1}{121 x ^{2} + 25} d x

\int_{- 4}^{4} (16 - x^{2} + 2) d x

\int_{3}^{4} - x^{3} + 7 x^{2} - 12 x d x

\int_{0}^{\infty} x ln (x) d x

\int_{- 5}^{0} 0 d x