What is the integral from 0 to 4 of 1/2 x ?

The integral from 0 to 4 of 1/2 x is 4

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integral from 0 to 4 of 1/2 x

\int_{0}^{4} \frac{1}{2} x d x

4

Solution steps

\int_{0}^{4} \frac{1}{2} x 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}^{4} x d x

Apply the Power Rule

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

= \frac{1}{2} [\frac{x ^{2}}{2}]_{0}^{4}

Compute the boundaries:

8

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

Simplify

= 4

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What is the integral from 0 to 4 of 1/2 x ?
The integral from 0 to 4 of 1/2 x is 4