de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from pi/2 to 0 of (1+cos(2t))/2

Lösung

\int_{\frac{π}{2}}^{0} \frac{1 + cos ( 2 t )}{2} d t

Lösung

- \frac{π}{4}

+1

Dezimale

- 0.78539 \dots

Schritte zur Lösung

\int_{\frac{π}{2}}^{0} \frac{1 + cos ( 2 t )}{2} d t

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

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

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

= - \frac{1}{2} (\frac{π}{2} + 0)

Vereinfache

- \frac{1}{2} (\frac{π}{2} + 0) : - \frac{π}{4}

= - \frac{π}{4}

Graph

Beliebte Beispiele

integral from 0 to 1 of 1/3

\int_{0}^{1} \frac{1}{3} d x

integral from 2 to 4 of 5

\int_{2}^{4} 5 d x

integral from 0 to 7 of tan(y)

\int_{0}^{7} tan (y) d y

integral from 0 to pi of 1/(cos^2(x))

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

integral from-2 to 5 of |t|

\int_{- 2}^{5} ∣ t ∣ d t