integral from 2 to 6 of 2400xsqrt(3+2x)

Lösung

\int_{2}^{6} 2400 x 3 + 2 x d x

- 33607 + 3600015

Dezimale

130537.67605 \dots

Schritte zur Lösung

\int_{2}^{6} 2400 x 3 + 2 x d x

Entferne die Konstante:

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

= 2400 \cdot \int_{2}^{6} x 3 + 2 x d x

Wende U-Substitution an

= 2400 \cdot \int_{7}^{15} \frac{u ( u - 3 )}{4} d u

Entferne die Konstante:

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

= 2400 \cdot \frac{1}{4} \cdot \int_{7}^{15} u (u - 3) d u

Multipliziere aus

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

= 2400 \cdot \frac{1}{4} \cdot \int_{7}^{15} 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

= 2400 \cdot \frac{1}{4} (\int_{7}^{15} u^{\frac{3}{2}} d u - \int_{7}^{15} 3 u d u)

\int_{7}^{15} u^{\frac{3}{2}} d u = 9015 - \frac{98 7}{5}

\int_{7}^{15} 3 u d u = 3015 - 147

= 2400 \cdot \frac{1}{4} (9015 - \frac{98 7}{5} - (3015 - 147))

Vereinfache

2400 \cdot \frac{1}{4} (9015 - \frac{98 7}{5} - (3015 - 147)) : - 33607 + 3600015

= - 33607 + 3600015

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