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

Lösung

\int_{- 1}^{1} 3 x^{2} x^{3} + 2 d x

23 - \frac{2}{3}

Dezimale

2.79743 \dots

Schritte zur Lösung

\int_{- 1}^{1} 3 x^{2} x^{3} + 2 d x

Entferne die Konstante:

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

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

Wende U-Substitution an

= 3 \cdot \int_{1}^{3} \frac{u}{3} d u

Entferne die Konstante:

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

= 3 \cdot \frac{1}{3} \cdot \int_{1}^{3} u d u

Wende die Potenzregel an

= 3 \cdot \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{3}

Vereinfache

3 \cdot \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{3} : [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{3}

= [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{3}

Berechne die Grenzen:

23 - \frac{2}{3}

= 23 - \frac{2}{3}

x \to - 1 lim (t^{2} - x^{2})

\int \frac{( x ^{2} - 3 x - 7 )}{( 2 x + 3 ) ( x + 1 ) ^{2}} d x

d er i v a t i v e 3 x^{4} - 6 x^{3} + 1

d er i v a t i v e f (x) = \frac{x ^{2} + 8}{9 x - 2}

d er i v a t i v e x^{10} e^{x}