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

The integral from 0 to t of y(u) is (yt^2)/2

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integral from 0 to t of y(u)

\int_{0}^{t} y (u) d u

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

Solution steps

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

Take the constant out:

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

= y \cdot \int_{0}^{t} u d u

Apply the Power Rule

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

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

Compute the boundaries:

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

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

Simplify

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

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What is the integral from 0 to t of y(u) ?
The integral from 0 to t of y(u) is (yt^2)/2