integral from 0 to x of 2(x+y)

Lösung

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

3 x^{2}

Schritte zur Lösung

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

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{x} x + y 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

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

\int_{0}^{x} x d y = x^{2}

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

= 2 (x^{2} + \frac{x ^{2}}{2})

Vereinfache

2 (x^{2} + \frac{x ^{2}}{2}) : 3 x^{2}

= 3 x^{2}

\int_{x}^{1} \frac{32}{9} (x y)^{\frac{1}{3}} d y

\int_{0}^{2} 1 + 4 x + x^{2} d x

\int_{1}^{5} e^{2 x - 1} d x

\int_{0}^{x^{2}} t^{2} e^{t^{2}} d t

\int_{0}^{4} \frac{x}{1 + x ^{2}} d x