What is the integral from 1 to 5 of k(5-x) ?

The integral from 1 to 5 of k(5-x) is 8k

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integral from 1 to 5 of k(5-x)

\int_{1}^{5} k (5 - x) d x

8 k

Solution steps

\int_{1}^{5} k (5 - x) d x

Take the constant out:

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

= k \cdot \int_{1}^{5} 5 - 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

= k (\int_{1}^{5} 5 d x - \int_{1}^{5} x d x)

\int_{1}^{5} 5 d x = 20

\int_{1}^{5} x d x = 12

= k (20 - 12)

Simplify

= 8 k

What is the integral from 1 to 5 of k(5-x) ?
The integral from 1 to 5 of k(5-x) is 8k