integral from 0 to 4 of pi(sqrt(y)+3)^2

Lösung

\int_{0}^{4} π (y + 3)^{2} d y

76 π

Dezimale

238.76104 \dots

Schritte zur Lösung

\int_{0}^{4} π (y + 3)^{2} d y

Entferne die Konstante:

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

= π \cdot \int_{0}^{4} (y + 3)^{2} d y

Multipliziere aus

(y + 3)^{2} : y + 6 y + 9

= π \cdot \int_{0}^{4} y + 6 y + 9 d y

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= π (\int_{0}^{4} y d y + \int_{0}^{4} 6 y d y + \int_{0}^{4} 9 d y)

\int_{0}^{4} y d y = 8

\int_{0}^{4} 6 y d y = 32

\int_{0}^{4} 9 d y = 36

= π (8 + 32 + 36)

Vereinfache

= 76 π

\int_{0}^{6} x^{2} + 2 d x

\int_{0}^{1} x^{2} + 2 x - 3 d x

\int_{0}^{120} 3 - 3 e^{- 0.15 x} d x

\int_{1}^{4} \frac{3 x - 2}{x} d x

\int_{0}^{2} 2 e^{2 x} d x