integral from 0 to 1 of x^4cos(x^5)

Lösung

\int_{0}^{1} x^{4} cos (x^{5}) d x

\frac{1}{5} sin (1)

Dezimale

0.16829 \dots

Schritte zur Lösung

\int_{0}^{1} x^{4} cos (x^{5}) d x

Wende U-Substitution an

= \int_{0}^{1} \frac{cos ( u )}{5} d u

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int_{0}^{1} cos (u) d u

Nutze das gemeinsame Integral :

\int cos (u) d u = sin (u)

= \frac{1}{5} [sin (u)]_{0}^{1}

Berechne die Grenzen:

sin (1)

= \frac{1}{5} sin (1)

\int_{0}^{2} 4 x cos (x^{2}) d x

\int_{0}^{4} \frac{x ^{2}}{2} d x

\int_{1}^{e^{5}} \frac{10 ln ( x )}{x} d x

\int_{0}^{3} (8 x - 1)^{2} d x

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