integral from 0 to x of (1-t^2)^{-1/2}

Lösung

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

arcsin (x)

Schritte zur Lösung

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

Trigonometrische Substitution anwenden

= \int_{0}^{a r c s i n (x)} 1 d u

Integral einer Konstanten :

\int a d x = a x

= [1 \cdot u]_{0}^{a r c s i n (x)}

Vereinfache

= [u]_{0}^{a r c s i n (x)}

Berechne die Grenzen:

arcsin (x)

= arcsin (x)

\int_{- 1}^{3} \frac{3 x ^{2}}{x ^{3} + 5} d x

\int_{- 1}^{1} \frac{3 x ^{2} - 1}{x ^{2}} d x

\int_{0}^{1} e^{x} cos (e^{x}) d x

\int_{6}^{8} \frac{1}{x ^{2}} d x

\int_{\frac{π}{4}}^{π} cos (x) d x