What is the integral from 0 to t of 2x ?

The integral from 0 to t of 2x is t^2

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integral from 0 to t of 2x

\int_{0}^{t} 2 x d x

t^{2}

Solution steps

\int_{0}^{t} 2 x d x

Take the constant out:

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

= 2 \cdot \int_{0}^{t} x d x

Apply the Power Rule

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

Compute the boundaries:

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

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

Simplify

= t^{2}