integral from 0 to 1 of (xarcsin(x^2))

Lösung

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

\frac{π}{4} - \frac{1}{2}

Dezimale

0.28539 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [\frac{1}{2} x^{2} arcsin (x^{2}) - \int \frac{x ^{3}}{1 - x ^{4}} d x]_{0}^{1}

\int \frac{x ^{3}}{1 - x ^{4}} d x = - \frac{1}{2} 1 - x^{4}

= [\frac{1}{2} x^{2} arcsin (x^{2}) - (- \frac{1}{2} 1 - x^{4})]_{0}^{1}

Vereinfache

[\frac{1}{2} x^{2} arcsin (x^{2}) - (- \frac{1}{2} 1 - x^{4})]_{0}^{1} : [\frac{1}{2} (x^{2} arcsin (x^{2}) + 1 - x^{4})]_{0}^{1}

= [\frac{1}{2} (x^{2} arcsin (x^{2}) + 1 - x^{4})]_{0}^{1}

Berechne die Grenzen:

\frac{π}{4} - \frac{1}{2}

= \frac{π}{4} - \frac{1}{2}

\int_{0}^{1} (5 x^{e} + 8 e^{x}) d x

\int \int 1 d x d x

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

\int \int x y d x d y

\int \int (x^{2} + y^{2}) d x d y