integral from 0 to 1 of (x-sqrt(1-x^2))

Lösung

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

\frac{1}{2} - \frac{π}{4}

Dezimale

- 0.28539 \dots

Schritte zur Lösung

\int_{0}^{1} x - 1 - x^{2} 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_{0}^{1} x d x - \int_{0}^{1} 1 - x^{2} d x

\int_{0}^{1} x d x = \frac{1}{2}

\int_{0}^{1} 1 - x^{2} d x = \frac{π}{4}

= \frac{1}{2} - \frac{π}{4}

\int_{- \infty}^{0} 4 x e^{5 x} d x

\int_{1}^{\infty} 2 e^{- 2 y} d y

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

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

\int_{0}^{4} y^{3} d y