What is the integral from 0 to 2 of f(x-2) ?

The integral from 0 to 2 of f(x-2) is -2f

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integral from 0 to 2 of f(x-2)

\int_{0}^{2} f (x - 2) d x

- 2 f

Solution steps

\int_{0}^{2} f (x - 2) d x

Take the constant out:

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

= f \cdot \int_{0}^{2} - 2 + 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_{0}^{2} 2 d x + \int_{0}^{2} x d x)

\int_{0}^{2} 2 d x = 4

\int_{0}^{2} x d x = 2

= f (- 4 + 2)

Simplify

= - 2 f

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What is the integral from 0 to 2 of f(x-2) ?
The integral from 0 to 2 of f(x-2) is -2f