What is the integral from 2 to 5 of (5x+2)/3 ?

The integral from 2 to 5 of (5x+2)/3 is 39/2

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integral from 2 to 5 of (5x+2)/3

\int_{2}^{5} \frac{5 x + 2}{3} d x

\frac{39}{2}

Decimal Notation

19.5

Solution steps

\int_{2}^{5} \frac{5 x + 2}{3} d x

Take the constant out:

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

= \frac{1}{3} \cdot \int_{2}^{5} 5 x + 2 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}{3} (\int_{2}^{5} 5 x d x + \int_{2}^{5} 2 d x)

\int_{2}^{5} 5 x d x = \frac{105}{2}

\int_{2}^{5} 2 d x = 6

= \frac{1}{3} (\frac{105}{2} + 6)

Simplify

\frac{1}{3} (\frac{105}{2} + 6) : \frac{39}{2}

= \frac{39}{2}

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What is the integral from 2 to 5 of (5x+2)/3 ?
The integral from 2 to 5 of (5x+2)/3 is 39/2