integral from-2pi to 2pi of xsin(0.5nx)

Lösung

\int_{- 2 π}^{2 π} x sin (0.5 n x) d x

- \frac{25.13274 \dots ( - 1 ) ^{n}}{n}

Schritte zur Lösung

\int_{- 2 π}^{2 π} x sin (0.5 n x) d x

Wende die partielle Integration an

= [\frac{1}{n} (- 2 x cos (0.5 n x) - n \cdot \int - \frac{2}{n} cos (0.5 n x) d x)]_{- 6.28318 \dots}^{2 π}

\int - \frac{2}{n} cos (0.5 n x) d x = - \frac{4}{n ^{2}} sin (0.5 n x)

= [\frac{1}{n} (- 2 x cos (0.5 n x) - n (- \frac{4}{n ^{2}} sin (0.5 n x)))]_{- 6.28318 \dots}^{2 π}

Vereinfache

[\frac{1}{n} (- 2 x cos (0.5 n x) - n (- \frac{4}{n ^{2}} sin (0.5 n x)))]_{- 6.28318 \dots}^{2 π} : [\frac{1}{n} (- 2 x cos (0.5 n x) + \frac{4}{n} sin (0.5 n x))]_{- 6.28318 \dots}^{2 π}

= [\frac{1}{n} (- 2 x cos (0.5 n x) + \frac{4}{n} sin (0.5 n x))]_{- 6.28318 \dots}^{2 π}

Berechne die Grenzen:

- (- 1)^{n} \frac{25.13274 \dots}{n}

= - (- 1)^{n} \frac{25.13274 \dots}{n}

Vereinfache

= - \frac{25.13274 \dots ( - 1 ) ^{n}}{n}

\int_{0}^{1} \frac{ln ( x ^{2} )}{x ^{2}} d x

\int_{0}^{2} 3 - \frac{4 e ^{0.28 t}}{e ^{0.28 t} + 10.13} d t

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

\int_{0}^{3} \frac{4 x ( 9 - x ^{2} )}{81} d x

\int_{0}^{2} (y + 2) d y