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

Lösung

\int_{- 2}^{2} (2 4 - x^{2})^{2} d x

\frac{128}{3}

Dezimale

42.66666 \dots

Schritte zur Lösung

\int_{- 2}^{2} (2 4 - x^{2})^{2} d x

Wende die partielle Integration an

= [4 x (4 - x^{2}) - \int - 8 x^{2} d x]_{- 2}^{2}

\int - 8 x^{2} d x = - \frac{8 x ^{3}}{3}

= [4 x (4 - x^{2}) - (- \frac{8 x ^{3}}{3})]_{- 2}^{2}

Vereinfache

= [4 x (4 - x^{2}) + \frac{8 x ^{3}}{3}]_{- 2}^{2}

Berechne die Grenzen:

\frac{128}{3}

= \frac{128}{3}

\frac{d}{d x} (\frac{( x ^{2} - 6 x )}{x + 1})

a re a y = \frac{2}{x}, y = 8 x, y = \frac{1}{8} x

\int_{2}^{\infty} \frac{1}{ln ( x )} d x

x \to \infty lim (- \frac{1}{2} e^{- x^{2}})

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