What is the integral from 0 to 4 of x/8 ?

The integral from 0 to 4 of x/8 is 1

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integral from 0 to 4 of x/8

\int_{0}^{4} \frac{x}{8} d x

1

Solution steps

\int_{0}^{4} \frac{x}{8} d x

Take the constant out:

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

= \frac{1}{8} \cdot \int_{0}^{4} x d x

Apply the Power Rule

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

= \frac{1}{8} [\frac{x ^{2}}{2}]_{0}^{4}

Compute the boundaries:

8

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

Simplify

= 1

f (x) = e^{x} - x e^{x}, at x = 0

x \to - 11 lim (x^{2} + 11)

x \to 0 lim (arctan (e^{x}))

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