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

The integral from 0 to 3 of f(3x) is (27f)/2

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integral from 0 to 3 of f(3x)

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

\frac{27 f}{2}

Solution steps

\int_{0}^{3} 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}^{3} x d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{9}{2}

= 3 f \frac{9}{2}

Simplify

= \frac{27 f}{2}

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What is the integral from 0 to 3 of f(3x) ?
The integral from 0 to 3 of f(3x) is (27f)/2