integral from 1 to 4 of ((1+sqrt(x))^{1/2})/(sqrt(x))

Lösung

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

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

Dezimale

3.15696 \dots

Schritte zur Lösung

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

Vereinfache

\frac{( 1 + x ) ^{\frac{1}{2}}}{x} : \frac{1 + x}{x}

= \int_{1}^{4} \frac{1 + x}{x} d x

Vereinfache

\frac{1 + x}{x} : \frac{1 + x}{x}

= \int_{1}^{4} \frac{1 + x}{x} d x

Wende U-Substitution an

= \int_{2}^{3} 2 u d u

Entferne die Konstante:

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

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

Wende die Potenzregel an

= 2 [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{3}

Berechne die Grenzen:

23 - \frac{4 2}{3}

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

\int_{- 2}^{2} \frac{x ^{2}}{2} - 3 d x

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

\int_{0}^{0.5} 1 - \frac{x}{2} d x

\int_{0}^{2 π} - sin (t) + cos (t) d t

\int_{0}^{1} - x^{2} + 36 d x