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Beliebt Rechnen >

integral from 0 to pi/2 of-10sin^2(3x)

Lösung

\int_{0}^{\frac{π}{2}} - 10 sin^{2} (3 x) d x

Lösung

- \frac{5 π}{2}

+1

Dezimale

- 7.85398 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} - 10 sin^{2} (3 x) d x

Entferne die Konstante:

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

= - 10 \cdot \int_{0}^{\frac{π}{2}} sin^{2} (3 x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= - 10 \cdot \int_{0}^{\frac{π}{2}} \frac{1}{2} (1 - cos (6 x)) d x

Entferne die Konstante:

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

= - 10 \cdot \frac{1}{2} \cdot \int_{0}^{\frac{π}{2}} 1 - cos (6 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

= - 10 \cdot \frac{1}{2} (\int_{0}^{\frac{π}{2}} 1 d x - \int_{0}^{\frac{π}{2}} cos (6 x) d x)

\int_{0}^{\frac{π}{2}} 1 d x = \frac{π}{2}

\int_{0}^{\frac{π}{2}} cos (6 x) d x = 0

= - 10 \cdot \frac{1}{2} (\frac{π}{2} - 0)

Vereinfache

- 10 \cdot \frac{1}{2} (\frac{π}{2} - 0) : - \frac{5 π}{2}

= - \frac{5 π}{2}

Graph

Beliebte Beispiele

integral of x/((sqrt(1+2x)))

\int \frac{x}{( 1 + 2 x )} d x

derivative of tan(6x^2)

\frac{d}{d x} (tan (6 x^{2}))

(\partial)/(\partial x)(cos^2(x-y))

\frac{\partial}{\partial x} (cos^{2} (x - y))

derivative of (x^2/(x-2))

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

integral from 4 to 6 of 2x

\int_{4}^{6} 2 x d x