integral from 0 to 3 of pi(2sqrt(7y))^2

Lösung

\int_{0}^{3} π (2 7 y)^{2} d y

π 126

Dezimale

395.84067 \dots

Schritte zur Lösung

\int_{0}^{3} π (2 7 y)^{2} d y

Entferne die Konstante:

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

= π \cdot \int_{0}^{3} (2 7 y)^{2} d y

Wende die partielle Integration an

= π [28 y^{2} - \int 28 y d y]_{0}^{3}

\int 28 y d y = 14 y^{2}

= π [28 y^{2} - 14 y^{2}]_{0}^{3}

Vereinfache

= π [14 y^{2}]_{0}^{3}

Berechne die Grenzen:

126

= π 126

\frac{d}{d x} (\frac{1}{( 3 ^{(- x^{2} - y^{2})} + 1 )})

y^{^{''}} - 0.2 y^{^{'}} + 0.01 y = 0, y (0) = 13, y^{^{'}} (0) = b

\frac{d ^{2}}{d x ^{2}} (x + 7 x)

\int \frac{1}{u ^{2} + 3} d u

\frac{d x}{d y} = \frac{y ^{3} - 3 x}{y}