What is the integral from 0.5 to 1.5 of 0.5x ?

The integral from 0.5 to 1.5 of 0.5x is 0.5

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integral from 0.5 to 1.5 of 0.5x

\int_{0.5}^{1.5} 0.5 x d x

0.5

Solution steps

\int_{0.5}^{1.5} 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_{0.5}^{1.5} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0.5}^{1.5}

= 0.5 [\frac{x ^{2}}{2}]_{0.5}^{1.5}

Simplify

= 0.5 [0.5 x^{2}]_{0.5}^{1.5}

Compute the boundaries:

1

= 0.5 \cdot 1

Simplify

= 0.5

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What is the integral from 0.5 to 1.5 of 0.5x ?
The integral from 0.5 to 1.5 of 0.5x is 0.5