integral from 4 to 10 of ((x-4)^2)/(72)

Lösung

\int_{4}^{10} \frac{( x - 4 ) ^{2}}{72} d x

1

Schritte zur Lösung

\int_{4}^{10} \frac{( x - 4 ) ^{2}}{72} d x

Entferne die Konstante:

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

= \frac{1}{72} \cdot \int_{4}^{10} (x - 4)^{2} d x

Multipliziere aus

(x - 4)^{2} : x^{2} - 8 x + 16

= \frac{1}{72} \cdot \int_{4}^{10} x^{2} - 8 x + 16 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{72} (\int_{4}^{10} x^{2} d x - \int_{4}^{10} 8 x d x + \int_{4}^{10} 16 d x)

\int_{4}^{10} x^{2} d x = 312

\int_{4}^{10} 8 x d x = 336

\int_{4}^{10} 16 d x = 96

= \frac{1}{72} (312 - 336 + 96)

Vereinfache

\frac{1}{72} (312 - 336 + 96) : 1

= 1

\frac{d ^{2}}{d x ^{2}} (\frac{7}{8 x ^{4}})

x \to 2 lim (\frac{7 x + 4}{3 x + 9})

\int \frac{( 3 ln ( x ) - 5 ) ^{4}}{x} d x

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\frac{d y}{d x} = x^{2} y