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

Lösung

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

x^{2} (- x + 1) + \frac{( - x + 1 ) ^{3}}{3}

Schritte zur Lösung

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

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

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

\int_{0}^{1 - x} y^{2} d y = \frac{( - x + 1 ) ^{3}}{3}

= x^{2} (- x + 1) + \frac{( - x + 1 ) ^{3}}{3}

\int_{2}^{4} - x^{3} + 7 x^{2} - 14 x + 8 d x

\int_{- 2}^{2} \frac{- 2}{( x - 1 ) ^{3}} d x

\int_{12}^{16} y^{2} - 6 d y

\int_{2}^{\infty} \frac{2}{v ^{2} - v} d v

\int_{0}^{b} m e^{- m x} d x