integral from 0 to 2x of 2xy^3-x

Lösung

\int_{0}^{2 x} 2 x y^{3} - x d y

- 2 x^{2} + 8 x^{5}

Schritte zur Lösung

\int_{0}^{2 x} 2 x y^{3} - x d y

Wende die Summenregel an:

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

= - \int_{0}^{2 x} x d y + \int_{0}^{2 x} 2 x y^{3} d y

\int_{0}^{2 x} x d y = 2 x^{2}

\int_{0}^{2 x} 2 x y^{3} d y = 8 x^{5}

= - 2 x^{2} + 8 x^{5}

\int_{- 1}^{1} ∣ x ∣ sin (x) d x

\int_{0}^{\frac{π}{2}} x sin (3 x) d x

\int_{0}^{4 π} ∣ sin (x) ∣ d x

\int_{0}^{2} 4 t^{2} + 1 d t

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