What is the integral from 0 to 5 of x 2/95 (12-x) ?

The integral from 0 to 5 of x 2/95 (12-x) is 130/57

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integral from 0 to 5 of x 2/95 (12-x)

\int_{0}^{5} x \frac{2}{95} (12 - x) d x

\frac{130}{57}

Decimal

2.28070 \dots

Solution steps

\int_{0}^{5} x \frac{2}{95} (12 - x) d x

Take the constant out:

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

= \frac{2}{95} \cdot \int_{0}^{5} x (12 - x) d x

Expand

x (12 - x) : 12 x - x^{2}

= \frac{2}{95} \cdot \int_{0}^{5} 12 x - x^{2} 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{2}{95} (\int_{0}^{5} 12 x d x - \int_{0}^{5} x^{2} d x)

\int_{0}^{5} 12 x d x = 150

\int_{0}^{5} x^{2} d x = \frac{125}{3}

= \frac{2}{95} (150 - \frac{125}{3})

Simplify

\frac{2}{95} (150 - \frac{125}{3}) : \frac{130}{57}

= \frac{130}{57}

What is the integral from 0 to 5 of x 2/95 (12-x) ?
The integral from 0 to 5 of x 2/95 (12-x) is 130/57