What is the integral from 2 to 4 of ((3x+14))/(46) ?

The integral from 2 to 4 of ((3x+14))/(46) is 1

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integral from 2 to 4 of ((3x+14))/(46)

\int_{2}^{4} \frac{( 3 x + 14 )}{46} d x

1

Solution steps

\int_{2}^{4} \frac{3 x + 14}{46} d x

Take the constant out:

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

= \frac{1}{46} \cdot \int_{2}^{4} 3 x + 14 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}{46} (\int_{2}^{4} 3 x d x + \int_{2}^{4} 14 d x)

\int_{2}^{4} 3 x d x = 18

\int_{2}^{4} 14 d x = 28

= \frac{1}{46} (18 + 28)

Simplify

\frac{1}{46} (18 + 28) : 1

= 1

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What is the integral from 2 to 4 of ((3x+14))/(46) ?
The integral from 2 to 4 of ((3x+14))/(46) is 1