integral from 0 to 3 of sqrt(4-4x+x^2)

Lösung

\int_{0}^{3} 4 - 4 x + x^{2} d x

\frac{5}{2}

Dezimale

2.5

Schritte zur Lösung

\int_{0}^{3} 4 - 4 x + x^{2} d x

Faktorisiere

4 - 4 x + x^{2} : (x - 2)^{2}

= \int_{0}^{3} (x - 2)^{2} d x

Wende Exponentenregel an:

a^{2} = ∣ a ∣

= \int_{0}^{3} (x - 2)^{2} d x

Entferne die Extremwerte

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

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

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

= 2 + \frac{1}{2}

Vereinfache

2 + \frac{1}{2} : \frac{5}{2}

= \frac{5}{2}

\int_{1}^{4} ∣ 3 x - 6 ∣ d x

\int_{- 1}^{3} \frac{1}{x} d x

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

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

\int_{0}^{2} 4 x (x^{2} + 3)^{3} d x