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Beliebt Rechnen >

integral from 0 to 4 of xsqrt(17-x^2)

Lösung

\int_{0}^{4} x 17 - x^{2} d x

Lösung

\frac{17 17 - 1}{3}

+1

Dezimale

23.03093 \dots

Schritte zur Lösung

\int_{0}^{4} x 17 - x^{2} d x

Wende U-Substitution an

= \int_{17}^{1} - \frac{u}{2} d u

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

= - \int_{1}^{17} - \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_{1}^{17} u d u)

Wende die Potenzregel an

= - (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{17})

Vereinfache

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{17}

Berechne die Grenzen:

\frac{34 17}{3} - \frac{2}{3}

= \frac{1}{2} (\frac{34 17}{3} - \frac{2}{3})

Vereinfache

= \frac{17 17 - 1}{3}

Graph

Beliebte Beispiele

integral from 0 to 1 of (x^4+6)/x

\int_{0}^{1} \frac{x ^{4} + 6}{x} d x

vereinfachen tan^4(2x-1)^3

s im pl i f y tan^{4} (2 x - 1)^{3}

integral of x/(x+1-sqrt(x+1))

\int \frac{x}{x + 1 - x + 1} d x

limit as x approaches 1+of 3/(ln(x))-2/(x-1)

x \to 1 + lim (\frac{3}{ln ( x )} - \frac{2}{x - 1})

tangent y= 4/x ,(5, 4/5)

t an g e n t y = \frac{4}{x}, (5, \frac{4}{5})