integral from 0 to 1 of x/(sqrt(4-x^2))

Lösung

\int_{0}^{1} \frac{x}{4 - x ^{2}} d x

2 - 3

Dezimale

0.26794 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{x}{4 - x ^{2}} d x

Wende U-Substitution an

= \int_{4}^{3} - \frac{1}{2 u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{3}^{4} - \frac{1}{2 u} d u

Entferne die Konstante:

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

= - (- \frac{1}{2} \cdot \int_{3}^{4} \frac{1}{u} d u)

Wende die Potenzregel an

= - (- \frac{1}{2} [2 u^{\frac{1}{2}}]_{3}^{4})

Vereinfache

- (- \frac{1}{2} [2 u^{\frac{1}{2}}]_{3}^{4}) : \frac{1}{2} [2 u]_{3}^{4}

= \frac{1}{2} [2 u]_{3}^{4}

Berechne die Grenzen:

4 - 23

= \frac{1}{2} (4 - 23)

Vereinfache

= 2 - 3

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 5 y = 0

\frac{d}{d x} (\frac{sin ^{2} ( x )}{cos ^{2} ( x )})

\int x^{a} d x

x \to 3 lim (- x^{2} + 5 x - 2)

\frac{d}{d x} (arcsin (x^{2} + y^{2} - 2))