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

Lösung

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

3 π

Dezimale

5.44139 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [\frac{1}{2} x 12 - 3 x^{2} - \int - \frac{3 x ^{2}}{2 12 - 3 x ^{2}} d x]_{- 2}^{2}

\int - \frac{3 x ^{2}}{2 12 - 3 x ^{2}} d x = - 3 (arcsin (\frac{x}{2}) - \frac{1}{2} sin (2 arcsin (\frac{x}{2})))

= [\frac{1}{2} x 12 - 3 x^{2} - (- 3 (arcsin (\frac{x}{2}) - \frac{1}{2} sin (2 arcsin (\frac{x}{2}))))]_{- 2}^{2}

Vereinfache

= [\frac{1}{2} x 12 - 3 x^{2} + 3 (arcsin (\frac{x}{2}) - \frac{1}{2} sin (2 arcsin (\frac{x}{2})))]_{- 2}^{2}

Berechne die Grenzen:

3 π

= 3 π

\int_{0}^{1} \frac{1}{( 2 x + 1 ) ^{2}} d x

\int_{0}^{1} t sin (t) d t

\int_{0}^{30} \frac{x}{4 + 2 x} d x

\int_{1}^{3} (x^{2} + 9) d x

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