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

Lösung

\int_{0}^{π} (x - sin^{2} (x)) d x

\frac{π ^{2} - π}{2}

Dezimale

3.36400 \dots

Schritte zur Lösung

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

\int_{0}^{π} x d x = \frac{π ^{2}}{2}

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

= \frac{π ^{2}}{2} - \frac{π}{2}

Da die Nenner gleich sind, fasse die Brüche zusammen.:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{π ^{2} - π}{2}

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

\int_{0}^{1} x (x^{2} - 1)^{4} d x

\int_{4}^{5} (\frac{2}{x} - x) d x

\int_{1}^{1.5} x^{2} + \frac{1}{4 x ^{2}} d x

\int_{- 1}^{0} \frac{x ^{15}}{x ^{8} + 1} d x