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Last Update: 11/22/2023 02:43 PM

Current Deck: Physikalische Rechenmethoden::Integrale und Ableitungen

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\(\int_{a}^{b}\(f'(x)=\sqrt{1-x^2} \sqrt{1-x^2} dx =\)

\(f(x)=?\)

Substituiere!
\(x = \sin(u), \; dx=\cos(u) \cdot du\)

\(\int_{\arcsin(a)}^{\arcsin(b)} \cos^2(u) du =\)

\(\frac{1}{2}[\sin(u) \cdot \cos(u) + u]_{\arcsin(a)}^{\arcsin(a)}\)
\(x = \sin(u), \; dx=\cos(u) \cdot du\)

\(\int_{\arcsin(a)}^{\arcsin(b)}\(f'(x)= \cos^2(u)\cos^2(u)\)

\(f(x) du= =\)
\(\frac{1}{2}[\sin(u)\frac{1}{2}[\sin(u) \cdot \cos(u) + u]_{\arcsin(a)}^{\arcsin(a)}\)