integral from 1 to 2 of xsin(pix^2)

Lösung

\int_{1}^{2} x sin (π x^{2}) d x

- \frac{1}{π}

Dezimale

- 0.31830 \dots

Schritte zur Lösung

\int_{1}^{2} x sin (π x^{2}) d x

Wende U-Substitution an

= \int_{π}^{4 π} \frac{sin ( u )}{2 π} d u

Entferne die Konstante:

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

= \frac{1}{2 π} \cdot \int_{π}^{4 π} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2 π} [- cos (u)]_{π}^{4 π}

Berechne die Grenzen:

- 2

= \frac{1}{2 π} (- 2)

Vereinfache

= - \frac{1}{π}

\int_{2}^{8} \frac{e ^{x}}{1 + e ^{x}} d x

\int_{- 4}^{1} x d x

\int_{0}^{4} \frac{1}{x ^{2} + 2 x - 8} d x

\int_{- R}^{R} R^{2} - x^{2} d x

\int_{0}^{3} - x^{2} + 4 x d x