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

The integral from 2 to 3 of 2x^2 is 38/3

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integral from 2 to 3 of 2x^2

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

\frac{38}{3}

Decimal

12.66666 \dots

Solution steps

\int_{2}^{3} 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_{2}^{3} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{2}^{3}

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

Compute the boundaries:

\frac{19}{3}

= 2 \cdot \frac{19}{3}

Simplify

= \frac{38}{3}

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What is the integral from 2 to 3 of 2x^2 ?
The integral from 2 to 3 of 2x^2 is 38/3