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Beliebt Rechnen >

integral from 0 to 1 of cos(npix)

Lösung

\int_{0}^{1} cos (nπ x) d x

Lösung

0

Schritte zur Lösung

\int_{0}^{1} cos (nπ x) d x

Wende U-Substitution an

= \int_{0}^{πn} \frac{cos ( u )}{πn} d u

Entferne die Konstante:

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

= \frac{1}{πn} \cdot \int_{0}^{πn} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{πn} [sin (u)]_{0}^{πn}

Berechne die Grenzen:

0

= \frac{1}{πn} \cdot 0

Vereinfache

= 0

Beliebte Beispiele

derivative of ln(6x^4-9x-3)

\frac{d}{d x} (ln (6 x^{4} - 9 x - 3))

y^{^{''}} + 8 y = 0

derivative of arctan(9^x)

\frac{d}{d x} (arctan (9^{x}))

(dx)/(dt)+2tx^3+x/t =0

\frac{d x}{d t} + 2 t x^{3} + \frac{x}{t} = 0

(\partial)/(\partial x)(3-(x^2+y^2)^{1/3})

\frac{\partial}{\partial x} (3 - (x^{2} + y^{2})^{\frac{1}{3}})