What is the integral from 0 to 2 of (5x^2) ?

The integral from 0 to 2 of (5x^2) is 40/3

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integral from 0 to 2 of (5x^2)

\int_{0}^{2} (5 x^{2}) d x

\frac{40}{3}

Decimal

13.33333 \dots

Solution steps

\int_{0}^{2} 5 x^{2} d x

Take the constant out:

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

= 5 \cdot \int_{0}^{2} x^{2} d x

Apply the Power Rule

= 5 [\frac{x ^{3}}{3}]_{0}^{2}

Compute the boundaries:

\frac{8}{3}

= 5 \cdot \frac{8}{3}

Simplify

= \frac{40}{3}

What is the integral from 0 to 2 of (5x^2) ?
The integral from 0 to 2 of (5x^2) is 40/3