integral from 0 to 4 of (sqrt(x)(x-1))

Lösung

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

\frac{112}{15}

Dezimale

7.46666 \dots

Schritte zur Lösung

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

Multipliziere aus

x (x - 1) : x^{\frac{3}{2}} - x

= \int_{0}^{4} x^{\frac{3}{2}} - x 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}^{4} x^{\frac{3}{2}} d x - \int_{0}^{4} x d x

\int_{0}^{4} x^{\frac{3}{2}} d x = \frac{64}{5}

\int_{0}^{4} x d x = \frac{16}{3}

= \frac{64}{5} - \frac{16}{3}

Vereinfache

\frac{64}{5} - \frac{16}{3} : \frac{112}{15}

= \frac{112}{15}

\int_{0}^{\frac{π}{2}} x (- cos (x) + 1) d x

\int_{0}^{0.8} \frac{1}{( 1 - x ) ^{2}} d x

\int_{2}^{4} \frac{2 ( 1 + x )}{27} d x

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

\int_{0}^{2} 3 4 x d x