integral from 0 to 1 of 2pi(x+1)(x^2)

Lösung

\int_{0}^{1} 2 π (x + 1) (x^{2}) d x

\frac{7 π}{6}

Dezimale

3.66519 \dots

Schritte zur Lösung

\int_{0}^{1} 2 π (x + 1) x^{2} d x

Entferne die Konstante:

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

= 2 π \cdot \int_{0}^{1} (x + 1) x^{2} d x

Multipliziere aus

(x + 1) x^{2} : x^{3} + x^{2}

= 2 π \cdot \int_{0}^{1} x^{3} + 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

= 2 π (\int_{0}^{1} x^{3} d x + \int_{0}^{1} x^{2} d x)

\int_{0}^{1} x^{3} d x = \frac{1}{4}

\int_{0}^{1} x^{2} d x = \frac{1}{3}

= 2 π (\frac{1}{4} + \frac{1}{3})

Vereinfache

2 π (\frac{1}{4} + \frac{1}{3}) : \frac{7 π}{6}

= \frac{7 π}{6}

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

\int \frac{1}{( x + 5 ) ^{2} ( x - 4 )} d x

d er i v a t i v e - 3 t

\frac{d}{d x} (6 sin (sin (x)))

\int sin^{3} (x co) s^{5} x d x