What is the integral from 7 to 25 of x(x-7)/(162) ?

The integral from 7 to 25 of x(x-7)/(162) is 19

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integral from 7 to 25 of x(x-7)/(162)

\int_{7}^{25} x \frac{x - 7}{162} d x

19

Solution steps

\int_{7}^{25} x \frac{x - 7}{162} d x

Take the constant out:

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

= \frac{1}{162} \cdot \int_{7}^{25} x (x - 7) d x

Expand

x (x - 7) : x^{2} - 7 x

= \frac{1}{162} \cdot \int_{7}^{25} x^{2} - 7 x d x

Apply the Sum Rule:

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

= \frac{1}{162} (\int_{7}^{25} x^{2} d x - \int_{7}^{25} 7 x d x)

\int_{7}^{25} x^{2} d x = 5094

\int_{7}^{25} 7 x d x = 2016

= \frac{1}{162} (5094 - 2016)

Simplify

\frac{1}{162} (5094 - 2016) : 19

= 19

What is the integral from 7 to 25 of x(x-7)/(162) ?
The integral from 7 to 25 of x(x-7)/(162) is 19