integral from 0 to 1 of (x^2-x^3)^2

Lösung

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

\frac{1}{105}

Dezimale

0.00952 \dots

Schritte zur Lösung

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

Multipliziere aus

(x^{2} - x^{3})^{2} : x^{4} - 2 x^{5} + x^{6}

= \int_{0}^{1} x^{4} - 2 x^{5} + x^{6} 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

= \int_{0}^{1} x^{4} d x - \int_{0}^{1} 2 x^{5} d x + \int_{0}^{1} x^{6} d x

\int_{0}^{1} x^{4} d x = \frac{1}{5}

\int_{0}^{1} 2 x^{5} d x = \frac{1}{3}

\int_{0}^{1} x^{6} d x = \frac{1}{7}

= \frac{1}{5} - \frac{1}{3} + \frac{1}{7}

Vereinfache

\frac{1}{5} - \frac{1}{3} + \frac{1}{7} : \frac{1}{105}

= \frac{1}{105}

\int_{- 2}^{0} x^{2} - 10 x d x

\int_{- π}^{π} t^{2} \cdot cos (n t) d t

\int_{- 1}^{2} e^{5 x - 4} d x

\int_{0}^{1} e^{- \frac{( x - 0.5 )}{2}} d x

\int_{1}^{4} (x^{2} - 4 x + 9) d x