integral from 0 to 2 of (x^3+1)^{1/2}x^2

Lösung

\int_{0}^{2} (x^{3} + 1)^{\frac{1}{2}} x^{2} d x

\frac{52}{9}

Dezimale

5.77777 \dots

Schritte zur Lösung

\int_{0}^{2} (x^{3} + 1)^{\frac{1}{2}} x^{2} d x

Wende U-Substitution an

= \int_{0}^{8} \frac{( u + 1 ) ^{\frac{1}{2}}}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{0}^{8} (u + 1)^{\frac{1}{2}} d u

Wende U-Substitution an

= \frac{1}{3} \cdot \int_{1}^{9} v^{\frac{1}{2}} d v

Wende die Potenzregel an

= \frac{1}{3} [\frac{2}{3} v^{\frac{3}{2}}]_{1}^{9}

Berechne die Grenzen:

\frac{52}{3}

= \frac{1}{3} \cdot \frac{52}{3}

Vereinfache

= \frac{52}{9}

s l o p e (- 5, - 2), (5, 14)

x \to - \frac{1}{4} lim (2)

x \to a lim ([2 f (3) - 3 g (4)])

y^{'} (t)

u \to 0 lim (6 - u^{2})