integral of integral of sqrt(1-x^2)

Lösung

\int \int 1 - x^{2} d x d x

\frac{1}{2} x arcsin (x) + \frac{1}{2} x^{2} 1 - x^{2} + \frac{1}{3} (- x^{2} + 1)^{\frac{3}{2}} + C x + C

Schritte zur Lösung

\int \int 1 - x^{2} d x d x

\int 1 - x^{2} d x = \frac{1}{2} (arcsin (x) + \frac{1}{2} sin (2 arcsin (x))) + C

= \int (\frac{1}{2} (arcsin (x) + \frac{1}{2} sin (2 arcsin (x))) + C) d x

\int (\frac{1}{2} (arcsin (x) + \frac{1}{2} sin (2 arcsin (x))) + C) d x = \frac{1}{2} x arcsin (x) + \frac{1}{2} x^{2} 1 - x^{2} + \frac{1}{3} (- x^{2} + 1)^{\frac{3}{2}} + C x + C

= \frac{1}{2} x arcsin (x) + \frac{1}{2} x^{2} 1 - x^{2} + \frac{1}{3} (- x^{2} + 1)^{\frac{3}{2}} + C x + C

\int \int (x + y + 1) d x d y

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