What is the integral from-0.5 to 0.5 of 1.5x^2 ?

The integral from-0.5 to 0.5 of 1.5x^2 is 0.125

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integral from-0.5 to 0.5 of 1.5x^2

\int_{- 0.5}^{0.5} 1.5 x^{2} d x

0.125

Solution steps

\int_{- 0.5}^{0.5} 1.5 x^{2} d x

Take the constant out:

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

= 1.5 \cdot \int_{- 0.5}^{0.5} x^{2} d x

Apply the Power Rule

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

= 1.5 [\frac{x ^{3}}{3}]_{- 0.5}^{0.5}

Simplify

= 1.5 [0.33333 \dots x^{3}]_{- 0.5}^{0.5}

Compute the boundaries:

0.08333 \dots

= 1.5 \cdot 0.08333 \dots

Simplify

= 0.125

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What is the integral from-0.5 to 0.5 of 1.5x^2 ?
The integral from-0.5 to 0.5 of 1.5x^2 is 0.125