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

The integral from 0 to t of f(t) is (ft^2)/2

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integral from 0 to t of f(t)

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

\frac{f t ^{2}}{2}

Solution steps

\int_{0}^{t} 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}^{t} t d t

Apply the Power Rule

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

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

Compute the boundaries:

\frac{t ^{2}}{2}

= f \frac{t ^{2}}{2}

Simplify

= \frac{f t ^{2}}{2}

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