integral from 0 to 100 of 2((x^2)-ax)

Lösung

\int_{0}^{100} 2 ((x^{2}) - a x) d x

2 (\frac{1000000}{3} - a \cdot 5000)

Schritte zur Lösung

\int_{0}^{100} 2 (x^{2} - a x) d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{100} x^{2} - a x 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

= 2 (\int_{0}^{100} x^{2} d x - \int_{0}^{100} a x d x)

\int_{0}^{100} x^{2} d x = \frac{1000000}{3}

\int_{0}^{100} a x d x = a \cdot 5000

= 2 (\frac{1000000}{3} - a \cdot 5000)

\int_{0}^{1} 2 x \cdot e^{x} d x

\int_{1}^{4} (3 x - 3 x) d x

\int_{2}^{7} (- \frac{x}{7} + \frac{9}{7}) - (\frac{2}{x}) d x

\int_{0}^{π} sin (x y) d x

\int_{1}^{5} \frac{4 x ^{3} - 1}{2 x - 1} d x