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Beliebt Rechnen >

f^'(x)=2sin(6x),f(pi/6)=-5/2

Lösung

f^{^{'}} (x) = 2 sin (6 x), f (\frac{π}{6}) = - \frac{5}{2}

Lösung

f (x) = - \frac{1}{3} cos (6 x) - \frac{17}{6}

Schritte zur Lösung

f^{'} (x) = 2 sin (6 x)

Wenn

f^{^{'}} (x) = g (x)

dann

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

f (x) = \int 2 sin (6 x) d x

\int 2 sin (6 x) d x = - \frac{1}{3} cos (6 x) + c_{1}

f (x) = - \frac{1}{3} cos (6 x) + c_{1}

Wende die Anfangsbedingung an:

f (x) = - \frac{1}{3} cos (6 x) - \frac{17}{6}

f (x) = - \frac{1}{3} cos (6 x) - \frac{17}{6}

Graph

Beliebte Beispiele

limit as x approaches 1 of sin(5pix)

x \to 1 lim (sin (5 p i x))

limit as x approaches 1+of (x^2+1)/(x-1)

x \to 1 + lim (\frac{x ^{2} + 1}{x - 1})

derivative 8x^3+2x+7x^{1/3}

d er i v a t i v e 8 x^{3} + 2 x + 7 x^{\frac{1}{3}}

integral of e^x+xe^x

\int e^{x} + x e^{x} d x

derivative of (x^2-2xe^x)

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