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

Lösung

\int_{0}^{2} π (4 - x^{2}) d x

π \frac{16}{3}

Dezimale

16.75516 \dots

Schritte zur Lösung

\int_{0}^{2} π (4 - x^{2}) d x

Entferne die Konstante:

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

= π \cdot \int_{0}^{2} 4 - x^{2} d x

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

\int_{0}^{2} 4 d x = 8

\int_{0}^{2} x^{2} d x = \frac{8}{3}

= π (8 - \frac{8}{3})

Füge

8 - \frac{8}{3}

zusammen:

\frac{16}{3}

= π \frac{16}{3}

\int_{1}^{3} \frac{π}{y} d y

\int_{0}^{l n (4)} e^{3 x} d x

\int_{1}^{4} x e^{6 x^{2} - 9} d x

\int_{\frac{1}{e}}^{e^{2}} \frac{x ^{3} + 1}{x} d x

\int_{0}^{1} 10 x 5^{x} d x