integral from 0 to pi/2 of 1/(3+cos(2a))

Lösung

\int_{0}^{\frac{π}{2}} \frac{1}{3 + cos ( 2 a )} d a

\frac{π}{4 2}

Dezimale

0.55536 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} \frac{1}{3 + cos ( 2 a )} d a

Berechne das unbestimmte Integral:

\int \frac{1}{3 + cos ( 2 a )} d a = \frac{1}{2 2} arctan (\frac{tan ( a )}{2}) + C

Berechne die Grenzen:

\int_{0}^{\frac{π}{2}} \frac{1}{3 + cos ( 2 a )} d a = \frac{π}{4 2} - 0

= \frac{π}{4 2} - 0

Vereinfache

= \frac{π}{4 2}

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