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Beliebt Rechnen >

integral from 0 to pi of sqrt(2-2cos(t))

Lösung

\int_{0}^{π} 2 - 2 cos (t) d t

Lösung

4

Schritte zur Lösung

\int_{0}^{π} 2 - 2 cos (t) d t

Wende U-Substitution an

= \int_{1}^{- 1} - \frac{2}{u + 1} d u

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

= - \int_{- 1}^{1} - \frac{2}{u + 1} d u

Entferne die Konstante:

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

= - (- \int_{- 1}^{1} \frac{2}{u + 1} d u)

Wende die partielle Integration an

= - - [\frac{2}{u + 1} u - \int - \frac{u}{2 ( u + 1 ) ^{\frac{3}{2}}} d u]_{- 1}^{1}

\int - \frac{u}{2 ( u + 1 ) ^{\frac{3}{2}}} d u = - \frac{2 ( u + 2 )}{u + 1}

= - - [\frac{2}{u + 1} u - (- \frac{2 ( u + 2 )}{u + 1})]_{- 1}^{1}

Vereinfache

- - [\frac{2}{u + 1} u - (- \frac{2 ( u + 2 )}{u + 1})]_{- 1}^{1} : [22 1 + u]_{- 1}^{1}

= [22 1 + u]_{- 1}^{1}

Berechne die Grenzen:

4

= 4

Graph

Beliebte Beispiele

integral from 0 to 2 of x/(1+10x^2)

\int_{0}^{2} \frac{x}{1 + 10 x ^{2}} d x

integral from 1 to 8 of (1/x)

\int_{1}^{8} (\frac{1}{x}) d x

integral from 0 to 2 of 4-x

\int_{0}^{2} 4 - x d x

integral from-3 to 1 of 8

\int_{- 3}^{1} 8 d x

integral from 1 to 2 of (4x^2)

\int_{1}^{2} (4 x^{2}) d x