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

The integral from 0 to 3x of f(t) is (9x^2f)/2

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integral from 0 to 3x of f(t)

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

\frac{9 x ^{2} f}{2}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

Compute the boundaries:

\frac{9 x ^{2}}{2}

= f \frac{9 x ^{2}}{2}

Simplify

= \frac{9 x ^{2} f}{2}

What is the integral from 0 to 3x of f(t) ?
The integral from 0 to 3x of f(t) is (9x^2f)/2