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

Lösung

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

\frac{π}{2}

Dezimale

1.57079 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} 1 + cos (2 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

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

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

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

= \frac{π}{2} + 0

Vereinfache

= \frac{π}{2}

\int_{2}^{3} (- 16 x + 2) d x

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

\int_{0}^{1} π (- x^{2} + 1)^{2} d x

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

\int_{0}^{1} \frac{x}{4} d x