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Beliebt Rechnen >

integral from 0 to 8 of pi(1-y/8)^2

Lösung

\int_{0}^{8} π (1 - \frac{y}{8})^{2} d y

Lösung

\frac{8 π}{3}

+1

Dezimale

8.37758 \dots

Schritte zur Lösung

\int_{0}^{8} π (1 - \frac{y}{8})^{2} d y

Entferne die Konstante:

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

= π \cdot \int_{0}^{8} (1 - \frac{y}{8})^{2} d y

Wende U-Substitution an

= π \cdot \int_{1}^{0} - 8 u^{2} d u

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

= π (- \int_{0}^{1} - 8 u^{2} d u)

Entferne die Konstante:

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

= π (- (- 8 \cdot \int_{0}^{1} u^{2} d u))

Wende die Potenzregel an

= π (- (- 8 [\frac{u ^{3}}{3}]_{0}^{1}))

Vereinfache

= 8 π [\frac{u ^{3}}{3}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{3}

= 8 π \frac{1}{3}

Vereinfache

= \frac{8 π}{3}

Graph

Beliebte Beispiele

integral of 1/(2x^2-x-3)

\int \frac{1}{2 x ^{2} - x - 3} d x

integral of sin^7(3/5 x)

\int sin^{7} (\frac{3}{5} x) d x

integral of x/(sqrt(x+9))

\int \frac{x}{x + 9} d x

integral of (3^{(2-x)}+(x+1)^2e^{(1-x)})

\int (3^{(2 - x)} + (x + 1)^{2} e^{(1 - x)}) d x

tangent y=3x^2-6,(-1,-3)

t an g e n t y = 3 x^{2} - 6, (- 1, - 3)