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

Lösung

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

\frac{21}{8}

Dezimale

2.625

Schritte zur Lösung

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

\int_{1}^{2} x^{2} d x = \frac{7}{3}

\int_{1}^{2} \frac{1}{x ^{4}} d x = \frac{7}{24}

= \frac{7}{3} + \frac{7}{24}

Vereinfache

\frac{7}{3} + \frac{7}{24} : \frac{21}{8}

= \frac{21}{8}

\int_{0}^{\frac{π}{4}} cos (x) - sin (x) d x

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

\int_{0}^{π} (1 - sin^{3} (x)) d x

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

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