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Beliebt Rechnen >

integral from-pi/2 to pi/2 of-sin^2(t)

Lösung

\int_{- \frac{π}{2}}^{\frac{π}{2}} - sin^{2} (t) d t

Lösung

- \frac{π}{2}

+1

Dezimale

- 1.57079 \dots

Schritte zur Lösung

\int_{- \frac{π}{2}}^{\frac{π}{2}} - sin^{2} (t) d t

Entferne die Konstante:

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

= - \int_{- \frac{π}{2}}^{\frac{π}{2}} sin^{2} (t) d t

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Entferne die Konstante:

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

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

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_{- \frac{π}{2}}^{\frac{π}{2}} 1 d t - \int_{- \frac{π}{2}}^{\frac{π}{2}} cos (2 t) d t)

\int_{- \frac{π}{2}}^{\frac{π}{2}} 1 d t = π

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

= - \frac{1}{2} (π - 0)

Vereinfache

- \frac{1}{2} (π - 0) : - \frac{π}{2}

= - \frac{π}{2}

Graph

Beliebte Beispiele

integral from 1 to 3 of x^2+3

\int_{1}^{3} x^{2} + 3 d x

integral from 0 to a of 10xsqrt(a^2-x^2)

\int_{0}^{a} 10 x a^{2} - x^{2} d x

integral from 3 to 2 of 1

\int_{3}^{2} 1

integral from 1/2 to 1 of (x^{-3}-15)

\int_{\frac{1}{2}}^{1} (x^{- 3} - 15) d x

integral from 0 to 5 of x+3

\int_{0}^{5} x + 3 d x