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Beliebt Rechnen >

integral from 0 to pi/6 of 2sec^3(x)

Lösung

\int_{0}^{\frac{π}{6}} 2 sec^{3} (x) d x

Lösung

2 (\frac{1}{3} + \frac{1}{4} ln (3))

+1

Dezimale

1.21597 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{6}} 2 sec^{3} (x) d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{\frac{π}{6}} sec^{3} (x) d x

Wende integrale Reduktion an

= 2 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{6}} + \frac{1}{2} \cdot \int_{0}^{\frac{π}{6}} sec (x) d x)

\int_{0}^{\frac{π}{6}} sec (x) d x = \frac{1}{2} ln (3)

= 2 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{6}} + \frac{1}{2} \cdot \frac{1}{2} ln (3))

Vereinfache

2 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{6}} + \frac{1}{2} \cdot \frac{1}{2} ln (3)) : 2 ([\frac{1}{2} sec (x) tan (x)]_{0}^{\frac{π}{6}} + \frac{1}{4} ln (3))

= 2 ([\frac{1}{2} sec (x) tan (x)]_{0}^{\frac{π}{6}} + \frac{1}{4} ln (3))

Berechne die Grenzen:

\frac{1}{3}

= 2 (\frac{1}{3} + \frac{1}{4} ln (3))

Graph

Beliebte Beispiele

integral of 1-e^{-x}

\int 1 - e^{- x} d x

integral from 1 to 7 of (x+1)/(x^2+2x-1)

\int_{1}^{7} \frac{x + 1}{x ^{2} + 2 x - 1} d x

derivative y=(pi^2x^6+9000)/(x^2)

d er i v a t i v e y = \frac{π ^{2} x ^{6} + 9000}{x ^{2}}

integral of 2tan^4(xse)c^6x

\int 2 tan^{4} (x se) c^{6} x d x

tangent f(x)=e^x,\at x=7

t an g e n t f (x) = e^{x}, at x = 7