What is the integral from 0 to 0.5 of 4x^2 ?

The integral from 0 to 0.5 of 4x^2 is 0.16666…

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integral from 0 to 0.5 of 4x^2

\int_{0}^{0.5} 4 x^{2} d x

0.16666 \dots

Solution steps

\int_{0}^{0.5} 4 x^{2} d x

Take the constant out:

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

= 4 \cdot \int_{0}^{0.5} x^{2} d x

Apply the Power Rule

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

= 4 [\frac{x ^{3}}{3}]_{0}^{0.5}

Simplify

= 4 [0.33333 \dots x^{3}]_{0}^{0.5}

Compute the boundaries:

0.04166 \dots

= 4 \cdot 0.04166 \dots

Simplify

= 0.16666 \dots

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What is the integral from 0 to 0.5 of 4x^2 ?
The integral from 0 to 0.5 of 4x^2 is 0.16666…