integral from 0 to 4 of xsqrt(16-x^2)

Lösung

\int_{0}^{4} x 16 - x^{2} d x

\frac{64}{3}

Dezimale

21.33333 \dots

Schritte zur Lösung

\int_{0}^{4} x 16 - x^{2} d x

Wende U-Substitution an

= \int_{16}^{0} - \frac{u}{2} d u

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

= - \int_{0}^{16} - \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}^{16} u d u)

Wende die Potenzregel an

= - (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{16})

Vereinfache

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{16}

Berechne die Grenzen:

\frac{128}{3}

= \frac{1}{2} \cdot \frac{128}{3}

Vereinfache

= \frac{64}{3}

\int \frac{1 - t}{t} d t

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = - 3

\frac{d}{d x} (3 sin^{2} (2 x))

\int sec (1) d x

x \to \frac{x}{4} lim (\frac{sin ( x )}{x})