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

The integral from 4 to-4 of (1/2 x+3) is -24

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

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

- 24

Solution steps

\int_{4}^{- 4} \frac{1}{2} x + 3 d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 4}^{4} \frac{1}{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

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

\int_{- 4}^{4} \frac{1}{2} x d x = 0

\int_{- 4}^{4} 3 d x = 24

= - (0 + 24)

Simplify

= - 24

What is the integral from 4 to-4 of (1/2 x+3) ?
The integral from 4 to-4 of (1/2 x+3) is -24