integral from 2 to 4 of x/(sqrt(x-1))

Lösung

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

2 (23 - \frac{4}{3})

Dezimale

4.26153 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{3} 2 (u^{2} + 1) d u

Entferne die Konstante:

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

= 2 \cdot \int_{1}^{3} u^{2} + 1 d u

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_{1}^{3} u^{2} d u + \int_{1}^{3} 1 d u)

\int_{1}^{3} u^{2} d u = 3 - \frac{1}{3}

\int_{1}^{3} 1 d u = 3 - 1

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

Vereinfache

2 (3 - \frac{1}{3} + 3 - 1) : 2 (23 - \frac{4}{3})

= 2 (23 - \frac{4}{3})

\int_{1}^{- 1} (3 r + 2)^{2} d r

\int_{0}^{4} (7 x^{2} - 8 x + 7) d x

\int_{- 1}^{1} 1 - \frac{8}{9 - x ^{2}} d x

\int_{1}^{7} \frac{2}{x} d x

\int_{0}^{- 1} 1