integral from 0 to pi of 3x^2sin(x^3)

Lösung

\int_{0}^{π} 3 x^{2} sin (x^{3}) d x

- cos (π^{3}) + 1

Dezimale

0.08273 \dots

Schritte zur Lösung

\int_{0}^{π} 3 x^{2} sin (x^{3}) d x

Entferne die Konstante:

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

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

Wende U-Substitution an

= 3 \cdot \int_{0}^{π^{3}} \frac{sin ( u )}{3} d u

Entferne die Konstante:

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

= 3 \cdot \frac{1}{3} \cdot \int_{0}^{π^{3}} sin (u) d u

Nutze das gemeinsame Integral :

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

= 3 \cdot \frac{1}{3} [- cos (u)]_{0}^{π^{3}}

Vereinfache

3 \cdot \frac{1}{3} [- cos (u)]_{0}^{π^{3}} : [- cos (u)]_{0}^{π^{3}}

= [- cos (u)]_{0}^{π^{3}}

Berechne die Grenzen:

- cos (π^{3}) + 1

= - cos (π^{3}) + 1

\int_{0}^{\frac{π}{2}} e^{x} + cos (x) d x

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