integral from 0 to 2pi of 1+sin^2(x)

Lösung

\int_{0}^{2 π} 1 + sin^{2} (x) d x

3 π

Dezimale

9.42477 \dots

Schritte zur Lösung

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

\int_{0}^{2 π} 1 d x = 2 π

\int_{0}^{2 π} sin^{2} (x) d x = π

= 2 π + π

Vereinfache

= 3 π

\int_{1}^{e} \frac{( 3 + ln ( x ) ) ^{4}}{x} d x

\int_{0}^{4 - y^{2}} (2 - z) d z

\int_{0}^{2} (x + 1)^{- 1} d x

\int_{0}^{5 - 2 x - \frac{1}{2} y} 6 z^{2} d z

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