integral from 0 to 5 of wsqrt(25-w^2)

Lösung

\int_{0}^{5} w 25 - w^{2} d w

\frac{125}{3}

Dezimale

41.66666 \dots

Schritte zur Lösung

\int_{0}^{5} w 25 - w^{2} d w

Wende U-Substitution an

= \int_{25}^{0} - \frac{u}{2} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{25} - \frac{u}{2} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - (- \frac{1}{2} \cdot \int_{0}^{25} u d u)

Wende die Potenzregel an

= - (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{25})

Vereinfache

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{25}

Berechne die Grenzen:

\frac{250}{3}

= \frac{1}{2} \cdot \frac{250}{3}

Vereinfache

= \frac{125}{3}

\int_{0}^{1} e^{- 5 t} d t

\int_{1}^{4} x (2 - x) d x

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

\int_{1}^{8} x^{- \frac{1}{3}} d x

\int_{0}^{2} (x - 3) (x - 5) d x