What is the integral from 3 to 7 of ((2x-3))/6 ?

The integral from 3 to 7 of ((2x-3))/6 is 14/3

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integral from 3 to 7 of ((2x-3))/6

\int_{3}^{7} \frac{( 2 x - 3 )}{6} d x

\frac{14}{3}

Decimal Notation

4.66666 \dots

Solution steps

\int_{3}^{7} \frac{2 x - 3}{6} 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_{3}^{7} 2 x - 3 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_{3}^{7} 2 x d x - \int_{3}^{7} 3 d x)

\int_{3}^{7} 2 x d x = 40

\int_{3}^{7} 3 d x = 12

= \frac{1}{6} (40 - 12)

Simplify

\frac{1}{6} (40 - 12) : \frac{14}{3}

= \frac{14}{3}

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\int (x + 2) e^{4 - 3 x} d x

n = 1 \sum \infty \frac{3 ^{n}}{n}

(t - 1) cos (4 (t - 1))

What is the integral from 3 to 7 of ((2x-3))/6 ?
The integral from 3 to 7 of ((2x-3))/6 is 14/3