integral from-5 to 0 of sin((npix)/5)

Lösung

\int_{- 5}^{0} sin (\frac{nπ x}{5}) d x

\frac{5 ( - 1 + ( - 1 ) ^{n} )}{πn}

Schritte zur Lösung

\int_{- 5}^{0} sin (\frac{nπ x}{5}) d x

Wende U-Substitution an

= \int_{- πn}^{0} \frac{5 sin ( u )}{πn} d u

Entferne die Konstante:

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

= \frac{5}{πn} \cdot \int_{- πn}^{0} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{5}{πn} [- cos (u)]_{- πn}^{0}

Berechne die Grenzen:

- 1 + (- 1)^{n}

= \frac{5}{πn} (- 1 + (- 1)^{n})

Vereinfache

= \frac{5 ( - 1 + ( - 1 ) ^{n} )}{πn}

\int_{1}^{2} [\frac{in x}{x ^{2}}] d x

\int_{0}^{t} sin (t - u) sin (u) d u

\int_{- 2}^{1} 6 - x^{2} d x

\int_{0}^{5} \frac{1}{x ^{0.5}} d x

\int_{- 3}^{1} 3 t^{3} + 2 t^{2} d t