What is the integral from 1 to 4 of 1/6 (x-1) ?

The integral from 1 to 4 of 1/6 (x-1) is 3/4

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integral from 1 to 4 of 1/6 (x-1)

\int_{1}^{4} \frac{1}{6} (x - 1) d x

\frac{3}{4}

Decimal Notation

0.75

Solution steps

\int_{1}^{4} \frac{1}{6} (x - 1) d x

Take the constant out:

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

= \frac{1}{6} \cdot \int_{1}^{4} x - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{6} (\int_{1}^{4} x d x - \int_{1}^{4} 1 d x)

\int_{1}^{4} x d x = \frac{15}{2}

\int_{1}^{4} 1 d x = 3

= \frac{1}{6} (\frac{15}{2} - 3)

Simplify

\frac{1}{6} (\frac{15}{2} - 3) : \frac{3}{4}

= \frac{3}{4}

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What is the integral from 1 to 4 of 1/6 (x-1) ?
The integral from 1 to 4 of 1/6 (x-1) is 3/4