integral from 0 to 0.5 of 7arccos(x)

Lösung

\int_{0}^{0.5} 7 arccos (x) d x

4.60301 \dots

Schritte zur Lösung

\int_{0}^{0.5} 7 arccos (x) d x

Entferne die Konstante:

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

= 7 \cdot \int_{0}^{0.5} arccos (x) d x

Wende die partielle Integration an

= 7 [x arccos (x) - \int - \frac{x}{1 - x ^{2}} d x]_{0}^{0.5}

\int - \frac{x}{1 - x ^{2}} d x = 1 - x^{2}

= 7 [x arccos (x) - 1 - x^{2}]_{0}^{0.5}

Berechne die Grenzen:

0.65757 \dots

= 7 \cdot 0.65757 \dots

Vereinfache

= 4.60301 \dots

x \to \infty lim (e^{+ x})

n = 0 \sum \infty (1 + \frac{1}{n})^{- n}

\int \frac{1}{( 5 x + 1 ) ^{3}} d x

\frac{d}{d x} (3 x^{4} - 5 x^{2} + 2 3 x)

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