What is the integral from 0 to x of 6x ?

The integral from 0 to x of 6x is 3x^2

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integral from 0 to x of 6x

\int_{0}^{x} 6 x d x

3 x^{2}

Solution steps

\int_{0}^{x} 6 x d x

Take the constant out:

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

= 6 \cdot \int_{0}^{x} x d x

Apply the Power Rule

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

= 6 [\frac{x ^{2}}{2}]_{0}^{x}

Compute the boundaries:

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

= 6 \cdot \frac{x ^{2}}{2}

Simplify

= 3 x^{2}

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