integral from-3 to 3 of (9-x^2)^{3/2}

Lösung

\int_{- 3}^{3} (9 - x^{2})^{\frac{3}{2}} d x

\frac{243 π}{8}

Dezimale

95.42587 \dots

Schritte zur Lösung

\int_{- 3}^{3} (9 - x^{2})^{\frac{3}{2}} d x

Wende die partielle Integration an

= [x (9 - x^{2})^{\frac{3}{2}} - \int - 3 x^{2} (9 - x^{2})^{\frac{1}{2}} d x]_{- 3}^{3}

\int - 3 x^{2} (9 - x^{2})^{\frac{1}{2}} d x = - 3 (\frac{1}{4} x^{3} (9 - x^{2})^{\frac{1}{2}} + \frac{81}{8} arcsin (\frac{1}{3} x) - \frac{81}{16} sin (2 arcsin (\frac{1}{3} x)))

= [x (9 - x^{2})^{\frac{3}{2}} - (- 3 (\frac{1}{4} x^{3} (9 - x^{2})^{\frac{1}{2}} + \frac{81}{8} arcsin (\frac{1}{3} x) - \frac{81}{16} sin (2 arcsin (\frac{1}{3} x))))]_{- 3}^{3}

Vereinfache

= [x (9 - x^{2})^{\frac{3}{2}} + 3 (\frac{1}{4} x^{3} (9 - x^{2})^{\frac{1}{2}} + \frac{81}{8} arcsin (\frac{1}{3} x) - \frac{81}{16} sin (2 arcsin (\frac{1}{3} x)))]_{- 3}^{3}

Berechne die Grenzen:

\frac{243 π}{8}

= \frac{243 π}{8}

\int_{0}^{l n (4)} e^{6 x} d x

\int_{0}^{x} \frac{1}{t} d t

\int_{0}^{\frac{8}{7}} \frac{1}{49 x ^{2} + 64} d x

\int_{0}^{3} (4 - 2 x) d x

\int_{2}^{4} 2^{3 x} d x