What is the integral from 5 to 7 of |f(3x)| ?

The integral from 5 to 7 of |f(3x)| is -36f

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integral from 5 to 7 of |f(3x)|

\int_{5}^{7} ∣ f (3 x) ∣ d x

- 36 f

Solution steps

\int_{5}^{7} ∣ f \cdot 3 x ∣ d x

Eliminate Absolutes

= \int_{5}^{7} - 3 f 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_{5}^{7} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{5}^{7}

= - 3 f [\frac{x ^{2}}{2}]_{5}^{7}

Compute the boundaries:

12

= - 3 f \cdot 12

Simplify

= - 36 f

\int_{0}^{15} x d x

\int_{0}^{1} (x + 3) e^{2 x} d x

\int_{3}^{7} 3 d x

\int_{1}^{4} - \frac{6}{x ^{2}} d x

\int_{3}^{7} 6 d x

What is the integral from 5 to 7 of |f(3x)| ?
The integral from 5 to 7 of |f(3x)| is -36f