What is the integral from 3 to 4 of (2(1+x))/(27) ?

The integral from 3 to 4 of (2(1+x))/(27) is 1/3

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integral from 3 to 4 of (2(1+x))/(27)

\int_{3}^{4} \frac{2 ( 1 + x )}{27} d x

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

\int_{3}^{4} \frac{2 ( 1 + x )}{27} d x

Take the constant out:

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

= \frac{2}{27} \cdot \int_{3}^{4} 1 + x 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{2}{27} (\int_{3}^{4} 1 d x + \int_{3}^{4} x d x)

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

\int_{3}^{4} x d x = \frac{7}{2}

= \frac{2}{27} (1 + \frac{7}{2})

Simplify

\frac{2}{27} (1 + \frac{7}{2}) : \frac{1}{3}

= \frac{1}{3}

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What is the integral from 3 to 4 of (2(1+x))/(27) ?
The integral from 3 to 4 of (2(1+x))/(27) is 1/3