integral from 0 to 1 of 4x^3(4-x^4)

Lösung

\int_{0}^{1} 4 x^{3} (4 - x^{4}) d x

\frac{7}{2}

Dezimale

3.5

Schritte zur Lösung

\int_{0}^{1} 4 x^{3} (4 - x^{4}) d x

Entferne die Konstante:

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

= 4 \cdot \int_{0}^{1} x^{3} (4 - x^{4}) d x

Multipliziere aus

x^{3} (4 - x^{4}) : 4 x^{3} - x^{7}

= 4 \cdot \int_{0}^{1} 4 x^{3} - x^{7} 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

= 4 (\int_{0}^{1} 4 x^{3} d x - \int_{0}^{1} x^{7} d x)

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

\int_{0}^{1} x^{7} d x = \frac{1}{8}

= 4 (1 - \frac{1}{8})

Vereinfache

4 (1 - \frac{1}{8}) : \frac{7}{2}

= \frac{7}{2}

\int_{0}^{1} \frac{1}{sin ( x )} d x

\int_{3.3}^{8.3} 12 x^{2} - 6 x + 4 d x

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

\int_{0}^{l n (3)} e^{5 x} d x

\int_{0}^{3} ∣ 3 x - 2 ∣ d x