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

Lösung

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

\frac{1}{4} (sin (16) - sin (1))

Dezimale

- 0.28234 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{16} \frac{cos ( u )}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{1}^{16} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{4} [sin (u)]_{1}^{16}

Berechne die Grenzen:

sin (16) - sin (1)

= \frac{1}{4} (sin (16) - sin (1))

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