What is the integral from-3 to 7 of (2x+6)/5 ?

The integral from-3 to 7 of (2x+6)/5 is 20

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integral from-3 to 7 of (2x+6)/5

\int_{- 3}^{7} \frac{2 x + 6}{5} d x

20

Solution steps

\int_{- 3}^{7} \frac{2 x + 6}{5} d x

Take the constant out:

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

= \frac{1}{5} \cdot \int_{- 3}^{7} 2 x + 6 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}{5} (\int_{- 3}^{7} 2 x d x + \int_{- 3}^{7} 6 d x)

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

\int_{- 3}^{7} 6 d x = 60

= \frac{1}{5} (40 + 60)

Simplify

\frac{1}{5} (40 + 60) : 20

= 20

What is the integral from-3 to 7 of (2x+6)/5 ?
The integral from-3 to 7 of (2x+6)/5 is 20