What is the integral from 0 to 4 of 2x^2 ?

The integral from 0 to 4 of 2x^2 is 128/3

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integral from 0 to 4 of 2x^2

\int_{0}^{4} 2 x^{2} d x

\frac{128}{3}

Decimal Notation

42.66666 \dots

Solution steps

\int_{0}^{4} 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}^{4} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{4}

= 2 [\frac{x ^{3}}{3}]_{0}^{4}

Compute the boundaries:

\frac{64}{3}

= 2 \cdot \frac{64}{3}

Simplify

= \frac{128}{3}

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What is the integral from 0 to 4 of 2x^2 ?
The integral from 0 to 4 of 2x^2 is 128/3