integral from 3 to 7 of xsqrt(x-3)

Lösung

\int_{3}^{7} x x - 3 d x

\frac{144}{5}

Dezimale

28.8

Schritte zur Lösung

\int_{3}^{7} x x - 3 d x

Wende U-Substitution an

= \int_{0}^{4} (u + 3) u d u

Multipliziere aus

(u + 3) u : u^{\frac{3}{2}} + 3 u

= \int_{0}^{4} u^{\frac{3}{2}} + 3 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}^{4} u^{\frac{3}{2}} d u + \int_{0}^{4} 3 u d u

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

\int_{0}^{4} 3 u d u = 16

= \frac{64}{5} + 16

Vereinfache

\frac{64}{5} + 16 : \frac{144}{5}

= \frac{144}{5}

\frac{d}{d x} (e^{c o s^{2} (x)})

\frac{d}{d x} (5 ln (x) + cos (x))

\int \frac{1}{x ^{2} + 14 x} d x

\int e^{2 u} d u

ma c l a u r in e^{x} \cdot sin (2 x)