What is the integral from 1 to 2 of (2x^2) ?

The integral from 1 to 2 of (2x^2) is 14/3

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integral from 1 to 2 of (2x^2)

\int_{1}^{2} (2 x^{2}) d x

\frac{14}{3}

Decimal

4.66666 \dots

Solution steps

\int_{1}^{2} 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_{1}^{2} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{1}^{2}

= 2 [\frac{x ^{3}}{3}]_{1}^{2}

Compute the boundaries:

\frac{7}{3}

= 2 \cdot \frac{7}{3}

Simplify

= \frac{14}{3}

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What is the integral from 1 to 2 of (2x^2) ?
The integral from 1 to 2 of (2x^2) is 14/3