What is the integral from 1 to 2 of (2x+1)/(12) ?

The integral from 1 to 2 of (2x+1)/(12) is 1/3

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integral from 1 to 2 of (2x+1)/(12)

\int_{1}^{2} \frac{2 x + 1}{12} d x

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

\int_{1}^{2} \frac{2 x + 1}{12} d x

Take the constant out:

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

= \frac{1}{12} \cdot \int_{1}^{2} 2 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}{12} (\int_{1}^{2} 2 x d x + \int_{1}^{2} 1 d x)

\int_{1}^{2} 2 x d x = 3

\int_{1}^{2} 1 d x = 1

= \frac{1}{12} (3 + 1)

Simplify

\frac{1}{12} (3 + 1) : \frac{1}{3}

= \frac{1}{3}

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What is the integral from 1 to 2 of (2x+1)/(12) ?
The integral from 1 to 2 of (2x+1)/(12) is 1/3