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

Lösung

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

8 x^{3} + 4 x^{2} + 4

Schritte zur Lösung

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

Wende die Summenregel an:

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

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

\int_{- 2}^{2 x} 3 t^{2} d t = 8 x^{3} + 8

\int_{- 2}^{2 x} 2 t d t = 2 (2 x^{2} - 2)

= 8 x^{3} + 8 + 2 (2 x^{2} - 2)

Vereinfache

8 x^{3} + 8 + 2 (2 x^{2} - 2) : 8 x^{3} + 4 x^{2} + 4

= 8 x^{3} + 4 x^{2} + 4

in v erse l a pl a ce \frac{3}{2 s + 1}

d er i v a t i v e f (x) = 2 x + 1

x \to 0 lim (\frac{sec ^{2} ( 3 x )}{2})

d er i v a t i v e f (x) = x^{3} + x^{2}

\frac{\partial}{\partial x} (x^{- 3} y^{- 4})