What is the integral from 0.5 to 1 of 3x^2 ?

The integral from 0.5 to 1 of 3x^2 is 0.87499…

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integral from 0.5 to 1 of 3x^2

\int_{0.5}^{1} 3 x^{2} d x

0.87499 \dots

Solution steps

\int_{0.5}^{1} 3 x^{2} d x

Take the constant out:

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

= 3 \cdot \int_{0.5}^{1} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0.5}^{1}

= 3 [\frac{x ^{3}}{3}]_{0.5}^{1}

Simplify

= 3 [0.33333 \dots x^{3}]_{0.5}^{1}

Compute the boundaries:

0.29166 \dots

= 3 \cdot 0.29166 \dots

Simplify

= 0.87499 \dots

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What is the integral from 0.5 to 1 of 3x^2 ?
The integral from 0.5 to 1 of 3x^2 is 0.87499…