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Beliebt Rechnen >

integral from 0 to 4 of sqrt(1+\sqrt{x)}

Lösung

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

Lösung

2 (\frac{2}{3} + \frac{18 3 - 2}{5} - 23)

+1

Dezimale

6.07589 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

Multipliziere aus

u (u - 1) : u^{\frac{3}{2}} - u

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

\int_{1}^{3} u^{\frac{3}{2}} d u = \frac{18 3 - 2}{5}

\int_{1}^{3} u d u = 23 - \frac{2}{3}

= 2 (\frac{18 3 - 2}{5} - (23 - \frac{2}{3}))

Vereinfache

= 2 (\frac{2}{3} + \frac{18 3 - 2}{5} - 23)

Graph

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