What is the integral from 0 to 2 of x x/2 ?

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

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integral from 0 to 2 of x x/2

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

\frac{4}{3}

Decimal Notation

1.33333 \dots

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{2} xx d x

Simplify

xx : x^{2}

= \frac{1}{2} \cdot \int_{0}^{2} x^{2} d x

Apply the Power Rule

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

= \frac{1}{2} [\frac{x ^{3}}{3}]_{0}^{2}

Compute the boundaries:

\frac{8}{3}

= \frac{1}{2} \cdot \frac{8}{3}

Simplify

= \frac{4}{3}

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\int_{1}^{4} 2 x - 4 d x

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