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

The integral from-3 to 6 of (-2/3 x+5) is 36

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

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

36

Solution steps

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

\int_{- 3}^{6} \frac{2}{3} x d x = 9

\int_{- 3}^{6} 5 d x = 45

= - 9 + 45

Simplify

= 36

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What is the integral from-3 to 6 of (-2/3 x+5) ?
The integral from-3 to 6 of (-2/3 x+5) is 36