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Beliebt Rechnen >

integral from 0 to pi of usin^2(u)

Lösung

\int_{0}^{π} u sin^{2} (u) d u

Lösung

\frac{π ^{2}}{4}

+1

Dezimale

2.46740 \dots

Schritte zur Lösung

\int_{0}^{π} u sin^{2} (u) d u

Wende die partielle Integration an

= [\frac{1}{4} (u (2 u - sin (2 u)) - 4 \cdot \int \frac{1}{2} (u - \frac{1}{2} sin (2 u)) d u)]_{0}^{π}

\int \frac{1}{2} (u - \frac{1}{2} sin (2 u)) d u = \frac{1}{2} (\frac{u ^{2}}{2} + \frac{1}{4} cos (2 u))

= [\frac{1}{4} (u (2 u - sin (2 u)) - 4 \cdot \frac{1}{2} (\frac{u ^{2}}{2} + \frac{1}{4} cos (2 u)))]_{0}^{π}

Vereinfache

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

= [\frac{1}{8} (2 u^{2} - 2 u sin (2 u) - cos (2 u))]_{0}^{π}

Berechne die Grenzen:

\frac{2 π ^{2} - 1}{8} + \frac{1}{8}

= \frac{2 π ^{2} - 1}{8} + \frac{1}{8}

Vereinfache

= \frac{π ^{2}}{4}

Graph

Beliebte Beispiele

(1+x^4)dy+(1+4y^2)dx=0

(1 + x^{4}) d y + (1 + 4 y^{2}) d x = 0

y^'-5y^{(2)}e^{(-3x)}=0,y(0)=9

y^{^{'}} - 5 y^{(2)} e^{(- 3 x)} = 0, y (0) = 9

integral of (x^3)/(x^2+2x+1)

\int \frac{x ^{3}}{x ^{2} + 2 x + 1} d x

tangent y=((x^2))/(8+sqrt(x))

t an g e n t y = \frac{( x ^{2} )}{8 + x}

integral of ((1-x^3))/(x\sqrt[3]{x)}

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