integral from-1 to 5 of (4x^3-3x^2+1)

Lösung

\int_{- 1}^{5} (4 x^{3} - 3 x^{2} + 1) d x

504

Schritte zur Lösung

\int_{- 1}^{5} 4 x^{3} - 3 x^{2} + 1 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 1}^{5} 4 x^{3} d x - \int_{- 1}^{5} 3 x^{2} d x + \int_{- 1}^{5} 1 d x

\int_{- 1}^{5} 4 x^{3} d x = 624

\int_{- 1}^{5} 3 x^{2} d x = 126

\int_{- 1}^{5} 1 d x = 6

= 624 - 126 + 6

Vereinfache

= 504

\int_{0}^{2} x e^{\frac{x ^{2}}{2}} d x

\int_{- 2}^{2} 10 4 - x^{2} d x

\int_{0}^{2} \frac{x ^{3}}{3} d x

\int_{- 1}^{1} x^{3} - 2 x^{2} + 5 d x

\int_{1}^{2} (x^{2} - 1)^{2} d x