integral from 4 to 5 of 3xsqrt(x^2-16)

Lösung

\int_{4}^{5} 3 x x^{2} - 16 d x

27

Schritte zur Lösung

\int_{4}^{5} 3 x x^{2} - 16 d x

Entferne die Konstante:

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

= 3 \cdot \int_{4}^{5} x x^{2} - 16 d x

Wende U-Substitution an

= 3 \cdot \int_{0}^{3} u^{2} d u

Wende die Potenzregel an

= 3 [\frac{u ^{3}}{3}]_{0}^{3}

Berechne die Grenzen:

9

= 3 \cdot 9

Vereinfache

= 27

\int_{2}^{3} \frac{7}{1 + x ^{2}} d x

\int_{- 5}^{0} (3 + ∣ x + 4 ∣) d x

\int_{- 1}^{3} 1 + (2 y + 1)^{2} d y

\int_{0}^{9 π} x (3 + sin (x)) d x

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