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Beliebt Rechnen >

integral from 0 to pi of 14sin^4(x)

Lösung

\int_{0}^{π} 14 sin^{4} (x) d x

Lösung

\frac{21 π}{4}

+1

Dezimale

16.49336 \dots

Schritte zur Lösung

\int_{0}^{π} 14 sin^{4} (x) d x

Entferne die Konstante:

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

= 14 \cdot \int_{0}^{π} sin^{4} (x) d x

Wende integrale Reduktion an

= 14 (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \int_{0}^{π} sin^{2} (x) d x)

\int_{0}^{π} sin^{2} (x) d x = \frac{π}{2}

= 14 (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \frac{π}{2})

Vereinfache

14 (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \frac{π}{2}) : 14 (- [\frac{1}{4} sin^{3} (x) cos (x)]_{0}^{π} + \frac{3 π}{8})

= 14 (- [\frac{1}{4} sin^{3} (x) cos (x)]_{0}^{π} + \frac{3 π}{8})

Berechne die Grenzen:

0

= 14 (- 0 + \frac{3 π}{8})

Vereinfache

= \frac{21 π}{4}

Graph

Beliebte Beispiele

integral of (x-1)/((x+1)^3)

\int \frac{x - 1}{( x + 1 ) ^{3}} d x

limit as x approaches 5 of x+3

x \to 5 lim (x + 3)

y^{^{'}} + 1 = 2 y

integral of x/((x^2-4)^3)

\int \frac{x}{( x ^{2} - 4 ) ^{3}} d x

derivative of (ax^2/(ln(x/4)))

\frac{d}{d x} (\frac{a x ^{2}}{ln ( \frac{x}{4} )})