What is the integral from 0.5 to 1 of 2x ?

The integral from 0.5 to 1 of 2x is 0.75

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integral from 0.5 to 1 of 2x

\int_{0.5}^{1} 2 x d x

0.75

Solution steps

\int_{0.5}^{1} 2 x d x

Take the constant out:

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

= 2 \cdot \int_{0.5}^{1} x d x

Apply the Power Rule

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

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

Simplify

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

Compute the boundaries:

0.375

= 2 \cdot 0.375

Simplify

= 0.75

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What is the integral from 0.5 to 1 of 2x ?
The integral from 0.5 to 1 of 2x is 0.75