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Beliebt Rechnen >

integral from 0 to a of sin^2((npix)/a)

Lösung

\int_{0}^{a} sin^{2} (\frac{nπ x}{a}) d x

Lösung

\frac{1}{2} (a - \frac{a sin ( 2 πn )}{2 πn})

Schritte zur Lösung

\int_{0}^{a} sin^{2} (\frac{nπ x}{a}) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{0}^{a} \frac{1}{2} (1 - cos (\frac{2 πn x}{a})) d x

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{a} 1 - cos (\frac{2 πn x}{a}) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int_{0}^{a} 1 d x - \int_{0}^{a} cos (\frac{2 πn x}{a}) d x)

\int_{0}^{a} 1 d x = a

\int_{0}^{a} cos (\frac{2 πn x}{a}) d x = \frac{a sin ( 2 πn )}{2 πn}

= \frac{1}{2} (a - \frac{a sin ( 2 πn )}{2 πn})

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derivative f(x)=-x^2+2

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\frac{d}{d x} (\frac{3}{2 - 3 x})

tangent f(x)=-1/x ,(3,-1/3)

t an g e n t f (x) = - \frac{1}{x}, (3, - \frac{1}{3})

(\partial)/(\partial x)(7xcos(3xy))

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\int \frac{12 x}{3 3 - x ^{2}} d x