What is the integral from 0 to 1 of 0.5x ?

The integral from 0 to 1 of 0.5x is 0.25

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integral from 0 to 1 of 0.5x

\int_{0}^{1} 0.5 x d x

0.25

Solution steps

\int_{0}^{1} 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}^{1} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{1}

= 0.5 [\frac{x ^{2}}{2}]_{0}^{1}

Simplify

= 0.5 [0.5 x^{2}]_{0}^{1}

Compute the boundaries:

0.5

= 0.5 \cdot 0.5

Simplify

= 0.25

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What is the integral from 0 to 1 of 0.5x ?
The integral from 0 to 1 of 0.5x is 0.25