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

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

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integral from 0 to 4 of x/4

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

2

Solution steps

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

Take the constant out:

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

= \frac{1}{4} \cdot \int_{0}^{4} x d x

Apply the Power Rule

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

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

Compute the boundaries:

8

= \frac{1}{4} \cdot 8

Simplify

= 2

\int_{- \infty}^{2} \frac{1}{x ^{2} + 4} d x

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\int_{0}^{4} \frac{1}{4 x ^{2} + 25} d x