What is the integral from 0.5 to 0.75 of 12x^2 ?

The integral from 0.5 to 0.75 of 12x^2 is 1.1875

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integral from 0.5 to 0.75 of 12x^2

\int_{0.5}^{0.75} 12 x^{2} d x

1.1875

Solution steps

\int_{0.5}^{0.75} 12 x^{2} d x

Take the constant out:

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

= 12 \cdot \int_{0.5}^{0.75} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0.5}^{0.75}

= 12 [\frac{x ^{3}}{3}]_{0.5}^{0.75}

Simplify

= 12 [0.33333 \dots x^{3}]_{0.5}^{0.75}

Compute the boundaries:

0.09895 \dots

= 12 \cdot 0.09895 \dots

Simplify

= 1.1875

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What is the integral from 0.5 to 0.75 of 12x^2 ?
The integral from 0.5 to 0.75 of 12x^2 is 1.1875