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

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

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integral from 0 to x of 2t

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

x^{2}

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{x ^{2}}{2}

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

Simplify

= x^{2}

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