integral of xsqrt(4-3x^2)

Lösung

\int x 4 - 3 x^{2} d x

- \frac{1}{9} (4 - 3 x^{2})^{\frac{3}{2}} + C

Schritte zur Lösung

\int x 4 - 3 x^{2} d x

Wende U-Substitution an

= \int - \frac{u}{6} d u

Entferne die Konstante:

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

= - \frac{1}{6} \cdot \int u d u

Wende die Potenzregel an

= - \frac{1}{6} \cdot \frac{2}{3} u^{\frac{3}{2}}

Setze in

u = 4 - 3 x^{2}

ein

= - \frac{1}{6} \cdot \frac{2}{3} (4 - 3 x^{2})^{\frac{3}{2}}

Vereinfache

- \frac{1}{6} \cdot \frac{2}{3} (4 - 3 x^{2})^{\frac{3}{2}} : - \frac{1}{9} (4 - 3 x^{2})^{\frac{3}{2}}

= - \frac{1}{9} (4 - 3 x^{2})^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{9} (4 - 3 x^{2})^{\frac{3}{2}} + C

\frac{\partial}{\partial x} (arcsin (\frac{x}{y ^{2}}))

d er i v a t i v e y = e^{π}

x \to \frac{π}{2} lim ((sin (x) - cos (x))^{t a n (x)})

\int 8 x e^{9 x} d x

x \to 0 lim (\frac{( 484 + x ) ^{0.5} - 22}{x})