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

Lösung

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

160

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Multipliziere aus

x (x^{2} + 5) : x^{3} + 5 x

= 4 \cdot \int_{1}^{3} x^{3} + 5 x 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

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

\int_{1}^{3} x^{3} d x = 20

\int_{1}^{3} 5 x d x = 20

= 4 (20 + 20)

Vereinfache

= 160

\int_{0}^{1} (x^{2} - 3 x + 2) d x

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

\int_{- 1}^{2} - x^{4} - x^{2} + 6 x + 8 d x

\int_{- 1}^{\infty} 3^{- x} d x

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