integral from 0 to x of x^2(-cos(xz)+1)

Lösung

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

x^{2} (x - \frac{sin ( x ^{2} )}{x})

Schritte zur Lösung

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

Entferne die Konstante:

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

= x^{2} \cdot \int_{0}^{x} 1 - cos (x z) d z

Wende die Summenregel an:

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

= x^{2} (\int_{0}^{x} 1 d z - \int_{0}^{x} cos (x z) d z)

\int_{0}^{x} 1 d z = x

\int_{0}^{x} cos (x z) d z = \frac{sin ( x ^{2} )}{x}

= x^{2} (x - \frac{sin ( x ^{2} )}{x})

\int_{0}^{2} ∣ x (x - 1) ∣ d x

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

\int_{0}^{\infty} k t e^{- k t} d t

\int_{- 5}^{0} - x^{2} - 5 x d x

\int_{π}^{3 π} sin (θ) d θ