What is the integral from 1 to 2 of f(2x) ?

The integral from 1 to 2 of f(2x) is 3f

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integral from 1 to 2 of f(2x)

\int_{1}^{2} f (2 x) d x

3 f

Solution steps

\int_{1}^{2} f \cdot 2 x d x

Take the constant out:

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

= 2 f \cdot \int_{1}^{2} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{1}^{2}

= 2 f [\frac{x ^{2}}{2}]_{1}^{2}

Compute the boundaries:

\frac{3}{2}

= 2 f \frac{3}{2}

Simplify

= 3 f

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What is the integral from 1 to 2 of f(2x) ?
The integral from 1 to 2 of f(2x) is 3f