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Beliebt Rechnen >

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

Lösung

\int_{0}^{π} sin^{2} (x) d x

Lösung

\frac{π}{2}

+1

Dezimale

1.57079 \dots

Schritte zur Lösung

\int_{0}^{π} sin^{2} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{0}^{π} \frac{1 - cos ( 2 x )}{2} d x

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{π} 1 - cos (2 x) d x

Wende die Summenregel an:

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

= \frac{1}{2} (\int_{0}^{π} 1 d x - \int_{0}^{π} cos (2 x) d x)

\int_{0}^{π} 1 d x = π

\int_{0}^{π} cos (2 x) d x = 0

= \frac{1}{2} (π - 0)

Vereinfache

\frac{1}{2} (π - 0) : \frac{π}{2}

= \frac{π}{2}

Graph

Beliebte Beispiele

(\partial)/(\partial x)(ln(4-x^2))

\frac{\partial}{\partial x} (ln (4 - x^{2}))

tangent y=4x^2-x^3,(1,3)

t an g e n t y = 4 x^{2} - x^{3}, (1, 3)

slopeintercept (0.1)(1.1)

s l o p e in t erce pt (0.1) (1.1)

limit as x approaches a of sqrt(0)

x \to a lim (0)

derivative f(x)=xsqrt(x+3)

d er i v a t i v e f (x) = x x + 3