What is the integral from 2 to 4 of f(x+6) ?

The integral from 2 to 4 of f(x+6) is 18f

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integral from 2 to 4 of f(x+6)

\int_{2}^{4} f (x + 6) d x

18 f

Solution steps

\int_{2}^{4} f (x + 6) d x

Take the constant out:

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

= f \cdot \int_{2}^{4} 6 + 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

= f (\int_{2}^{4} 6 d x + \int_{2}^{4} x d x)

\int_{2}^{4} 6 d x = 12

\int_{2}^{4} x d x = 6

= f (12 + 6)

Simplify

= 18 f

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What is the integral from 2 to 4 of f(x+6) ?
The integral from 2 to 4 of f(x+6) is 18f