integral from 0 to 4 of x^3sqrt(x^2+16)

Lösung

\int_{0}^{4} x^{3} x^{2} + 16 d x

\frac{2048 2 + 2048}{15}

Dezimale

329.62062 \dots

Schritte zur Lösung

\int_{0}^{4} x^{3} x^{2} + 16 d x

Wende U-Substitution an

= \int_{4}^{42} (u^{2} - 16) u^{2} d u

Multipliziere aus

(u^{2} - 16) u^{2} : u^{4} - 16 u^{2}

= \int_{4}^{42} u^{4} - 16 u^{2} 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_{4}^{42} u^{4} d u - \int_{4}^{42} 16 u^{2} d u

\int_{4}^{42} u^{4} d u = \frac{4096 2 - 1024}{5}

\int_{4}^{42} 16 u^{2} d u = \frac{16 ( 128 2 - 64 )}{3}

= \frac{4096 2 - 1024}{5} - \frac{16 ( 128 2 - 64 )}{3}

Vereinfache

\frac{4096 2 - 1024}{5} - \frac{16 ( 128 2 - 64 )}{3} : \frac{2048 2 + 2048}{15}

= \frac{2048 2 + 2048}{15}

\frac{d}{d x} (3 x^{2} + 2 x + 1)

t^{2} y^{^{'}} + t y = 5

l a pl a ce t r an s f or m x sin (3 x)

\frac{d}{d x} (\frac{1}{e ^{x} + 1})

t a y l or x \cdot ln (x)