What is the integral from 0 to x of 0.5x ?

The integral from 0 to x of 0.5x is 0.25x^2

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integral from 0 to x of 0.5x

\int_{0}^{x} 0.5 x d x

0.25 x^{2}

Solution steps

\int_{0}^{x} 0.5 x d x

Take the constant out:

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

= 0.5 \cdot \int_{0}^{x} x d x

Apply the Power Rule

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

= 0.5 [\frac{x ^{2}}{2}]_{0}^{x}

Simplify

= 0.5 [0.5 x^{2}]_{0}^{x}

Compute the boundaries:

0.5 x^{2}

= 0.5 \cdot 0.5 x^{2}

Simplify

= 0.25 x^{2}

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What is the integral from 0 to x of 0.5x ?
The integral from 0 to x of 0.5x is 0.25x^2