What is the integral from 1.5 to 2 of (2x)/3 ?

The integral from 1.5 to 2 of (2x)/3 is 0.58333…

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integral from 1.5 to 2 of (2x)/3

\int_{1.5}^{2} \frac{2 x}{3} d x

0.58333 \dots

Solution steps

\int_{1.5}^{2} \frac{2 x}{3} d x

Take the constant out:

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

= \frac{2}{3} \cdot \int_{1.5}^{2} x d x

Apply the Power Rule

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

= \frac{2}{3} [\frac{x ^{2}}{2}]_{1.5}^{2}

Simplify

= 0.66666 \dots [0.5 x^{2}]_{1.5}^{2}

Compute the boundaries:

0.875

= 0.66666 \dots \cdot 0.875

Simplify

= 0.58333 \dots

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What is the integral from 1.5 to 2 of (2x)/3 ?
The integral from 1.5 to 2 of (2x)/3 is 0.58333…