integral from 1 to 2 of 3/(sqrt(4x-x^2))

Lösung

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

\frac{π}{2}

Dezimale

1.57079 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Vervollständige das Quadrat

4 x - x^{2} : - (x - 2)^{2} + 4

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

Wende U-Substitution an

= 3 \cdot \int_{- 1}^{0} \frac{1}{- u ^{2} + 4} d u

Trigonometrische Substitution anwenden

= 3 \cdot \int_{- \frac{π}{6}}^{0} 1 d v

Integral einer Konstanten :

\int a d x = a x

= 3 [1 \cdot v]_{- \frac{π}{6}}^{0}

Vereinfache

= 3 [v]_{- \frac{π}{6}}^{0}

Berechne die Grenzen:

\frac{π}{6}

= 3 \cdot \frac{π}{6}

Vereinfache

= \frac{π}{2}

t an g e n t f (x) = x - 4, at x = 13

y^{^{'}} = - \frac{2 x}{y}

\frac{d y}{d x} = \frac{8 x}{5 y}

\int (x^{2} + 4)^{2} d x

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