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

The integral from 0 to 2 of 2t is 4

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integral from 0 to 2 of 2t

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

4

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

Compute the boundaries:

2

= 2 \cdot 2

Simplify

= 4