integral from-pi to pi of x^2cos(2x)

Lösung

\int_{- π}^{π} x^{2} cos (2 x) d x

π

Dezimale

3.14159 \dots

Schritte zur Lösung

\int_{- π}^{π} x^{2} cos (2 x) d x

Wende die partielle Integration an

= [\frac{1}{2} (x^{2} sin (2 x) - 2 \cdot \int x sin (2 x) d x)]_{- π}^{π}

\int x sin (2 x) d x = - \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x)

= [\frac{1}{2} (x^{2} sin (2 x) - 2 (- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x)))]_{- π}^{π}

Vereinfache

[\frac{1}{2} (x^{2} sin (2 x) - 2 (- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x)))]_{- π}^{π} : [\frac{1}{4} (2 x^{2} sin (2 x) + 2 x cos (2 x) - sin (2 x))]_{- π}^{π}

= [\frac{1}{4} (2 x^{2} sin (2 x) + 2 x cos (2 x) - sin (2 x))]_{- π}^{π}

Berechne die Grenzen:

π

= π

d er i v a t i v e 6 (5)^{2} - 2 (5) + 9

\frac{d}{d x} (e^{2 x} + x^{2} - 16)

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

in v erse l a pl a ce \frac{s ^{2} + 8}{( s + 2 ) ^{4}}

n = - 4 \sum \infty (- \frac{4}{11})^{n}