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Beliebt Rechnen >

integral from 0 to pi/2 of x^2sin(x)

Lösung

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

Lösung

π - 2

+1

Dezimale

1.14159 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [- x^{2} cos (x) - \int - 2 x cos (x) d x]_{0}^{\frac{π}{2}}

\int - 2 x cos (x) d x = - 2 (x sin (x) + cos (x))

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

Vereinfache

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

Berechne die Grenzen:

π - 2

= π - 2

Graph

Beliebte Beispiele

limit as x approaches infinity of (2x^2)/(x+3)

x \to \infty lim (\frac{2 x ^{2}}{x + 3})

derivative of ln(x^3-2x^2)

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

integral of cos(0)

\int cos (0)

y^'=(e^{x+y})/(1+e^x),y(1)=0

y^{^{'}} = \frac{e ^{x + y}}{1 + e ^{x}}, y (1) = 0

integral of 2^{2-2x}

\int 2^{2 - 2 x} d x