integral from 0 to 1/2 of 7arccos(x)

Lösung

\int_{0}^{\frac{1}{2}} 7 arccos (x) d x

7 (\frac{π}{6} - \frac{3}{2} + 1)

Dezimale

4.60301 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Berechne die Grenzen:

\frac{π}{6} - \frac{3}{2} + 1

= 7 (\frac{π}{6} - \frac{3}{2} + 1)

y^{^{'}} = 14 x y - 2 x

y^{^{''}} + 4 y^{^{'}} + 5 y = - 5 x + 5 e^{- x}

x y^{^{'}} + y = y^{2}, y (1) = - 5

\frac{d}{d x} (7 x^{3})

n = 1 \sum \infty \frac{8 n}{- 2 n + 9}