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

The integral from 2 to 4 of 2x^2 is 112/3

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integral from 2 to 4 of 2x^2

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

\frac{112}{3}

Decimal

37.33333 \dots

Solution steps

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

Apply the Power Rule

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

Compute the boundaries:

\frac{56}{3}

= 2 \cdot \frac{56}{3}

Simplify

= \frac{112}{3}

What is the integral from 2 to 4 of 2x^2 ?
The integral from 2 to 4 of 2x^2 is 112/3