What is the integral from 0 to 2 of f(3x) ?

The integral from 0 to 2 of f(3x) is 6f

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integral from 0 to 2 of f(3x)

\int_{0}^{2} f (3 x) d x

6 f

Solution steps

\int_{0}^{2} f \cdot 3 x d x

Take the constant out:

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

= 3 f \cdot \int_{0}^{2} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{2}

= 3 f [\frac{x ^{2}}{2}]_{0}^{2}

Compute the boundaries:

2

= 3 f \cdot 2

Simplify

= 6 f

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What is the integral from 0 to 2 of f(3x) ?
The integral from 0 to 2 of f(3x) is 6f