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

The integral from 0 to x of x/2 is (x^2)/4

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integral from 0 to x of x/2

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

\frac{x ^{2}}{4}

Solution steps

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

Apply the Power Rule

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

Compute the boundaries:

\frac{x ^{2}}{2}

= \frac{1}{2} \cdot \frac{x ^{2}}{2}

Simplify

= \frac{x ^{2}}{4}

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\int_{0}^{2} x cos (\frac{nπ x}{2}) d x

\int_{0}^{5} \frac{x ^{3}}{x ^{2} + 1} d x

\int_{2}^{3} 4 x e^{x^{2} - 5} d x

What is the integral from 0 to x of x/2 ?
The integral from 0 to x of x/2 is (x^2)/4