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

The integral from 0 to t of i(t) is (it^2)/2

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integral from 0 to t of i(t)

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

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

Solution steps

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

Take the constant out:

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

= i \cdot \int_{0}^{t} t d t

Apply the Power Rule

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

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

Compute the boundaries:

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

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

Simplify

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

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