integral from 6 to 7 of (tsqrt(t-6))

Lösung

\int_{6}^{7} (t t - 6) d t

\frac{22}{5}

Dezimale

4.4

Schritte zur Lösung

\int_{6}^{7} t t - 6 d t

Wende U-Substitution an

= \int_{0}^{1} (u + 6) u d u

Multipliziere aus

(u + 6) u : u^{\frac{3}{2}} + 6 u

= \int_{0}^{1} u^{\frac{3}{2}} + 6 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}^{1} u^{\frac{3}{2}} d u + \int_{0}^{1} 6 u d u

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

\int_{0}^{1} 6 u d u = 4

= \frac{2}{5} + 4

Vereinfache

\frac{2}{5} + 4 : \frac{22}{5}

= \frac{22}{5}

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

y^{^{'}} = 3 (y + 1)

d er i v a t i v e \frac{cos ( x )}{sin ( x )}

a re a y = 10 x^{3}, y = 10 x^{2}

\int \frac{1}{2 x ^{3}} d x