What is the integral from 0 to 6 of 2x^2 ?

The integral from 0 to 6 of 2x^2 is 144

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integral from 0 to 6 of 2x^2

\int_{0}^{6} 2 x^{2} d x

144

Solution steps

\int_{0}^{6} 2 x^{2} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{6} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{6}

= 2 [\frac{x ^{3}}{3}]_{0}^{6}

Compute the boundaries:

72

= 2 \cdot 72

Simplify

= 144

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What is the integral from 0 to 6 of 2x^2 ?
The integral from 0 to 6 of 2x^2 is 144