integral from 1 to 2 of 4x^3+3x^2+4x+2

Lösung

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

30

Schritte zur Lösung

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

\int_{1}^{2} 4 x^{3} d x = 15

\int_{1}^{2} 3 x^{2} d x = 7

\int_{1}^{2} 4 x d x = 6

\int_{1}^{2} 2 d x = 2

= 15 + 7 + 6 + 2

Vereinfache

= 30

\int_{0}^{2 π} x \cdot sin (n x) d x

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

\int_{0}^{\frac{x}{3}} sin (3 t) d t

\int_{0}^{1} e^{- r^{2}} r d r

\int_{- π}^{π} sin (n t) d t