What is the integral from 0 to 0.5 of 3x^2 ?

The integral from 0 to 0.5 of 3x^2 is 0.125

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integral from 0 to 0.5 of 3x^2

\int_{0}^{0.5} 3 x^{2} d x

0.125

Solution steps

\int_{0}^{0.5} 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}^{0.5} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{0.5}

= 3 [\frac{x ^{3}}{3}]_{0}^{0.5}

Simplify

= 3 [0.33333 \dots x^{3}]_{0}^{0.5}

Compute the boundaries:

0.04166 \dots

= 3 \cdot 0.04166 \dots

Simplify

= 0.125

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What is the integral from 0 to 0.5 of 3x^2 ?
The integral from 0 to 0.5 of 3x^2 is 0.125