integral from 0 to 5 of rsqrt(25-r^2)

Lösung

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

\frac{125}{3}

Dezimale

41.66666 \dots

Schritte zur Lösung

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

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_{x}^{x^{2}} (\frac{y}{x}) d y

\int_{0}^{6} \frac{∣ 2 x - 5 ∣}{x + 1} d x

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

\int_{0}^{6} x d x

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