integral from 4 to 6 of x^2sqrt(x-4)

Lösung

\int_{4}^{6} x^{2} x - 4 d x

\frac{3824 2}{105}

Dezimale

51.50431 \dots

Schritte zur Lösung

\int_{4}^{6} x^{2} x - 4 d x

Wende U-Substitution an

= \int_{0}^{2} (u + 4)^{2} u d u

Multipliziere aus

(u + 4)^{2} u : u^{\frac{5}{2}} + 8 u^{\frac{3}{2}} + 16 u

= \int_{0}^{2} u^{\frac{5}{2}} + 8 u^{\frac{3}{2}} + 16 u d u

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}^{2} u^{\frac{5}{2}} d u + \int_{0}^{2} 8 u^{\frac{3}{2}} d u + \int_{0}^{2} 16 u d u

\int_{0}^{2} u^{\frac{5}{2}} d u = \frac{16 2}{7}

\int_{0}^{2} 8 u^{\frac{3}{2}} d u = \frac{64 2}{5}

\int_{0}^{2} 16 u d u = \frac{64 2}{3}

= \frac{16 2}{7} + \frac{64 2}{5} + \frac{64 2}{3}

Vereinfache

\frac{16 2}{7} + \frac{64 2}{5} + \frac{64 2}{3} : \frac{3824 2}{105}

= \frac{3824 2}{105}

\int_{2}^{4} (x y^{2} + x^{2} + y + 4) d y

\int_{- 5}^{- 3} x^{2} - 4 d x

\int_{0}^{4} x (3 - 5 x) d x

\int_{0}^{8} 6 x ln (x) d x

\int_{0.5}^{1} 2 x d x