integral from 1 to 3 of 15xsqrt(x+3)

Lösung

\int_{1}^{3} 15 x x + 3 d x

366 + 48

Dezimale

136.18163 \dots

Schritte zur Lösung

\int_{1}^{3} 15 x x + 3 d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 15 \cdot \int_{1}^{3} x x + 3 d x

Wende U-Substitution an

= 15 \cdot \int_{4}^{6} (u - 3) u d u

Multipliziere aus

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

= 15 \cdot \int_{4}^{6} 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

= 15 (\int_{4}^{6} u^{\frac{3}{2}} d u - \int_{4}^{6} 3 u d u)

\int_{4}^{6} u^{\frac{3}{2}} d u = \frac{72 6 - 64}{5}

\int_{4}^{6} 3 u d u = 126 - 16

= 15 (\frac{72 6 - 64}{5} - (126 - 16))

Vereinfache

15 (\frac{72 6 - 64}{5} - (126 - 16)) : 366 + 48

= 366 + 48