What is the integral from 1.5 to 3 of (-x/3+1) ?

The integral from 1.5 to 3 of (-x/3+1) is 0.375

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integral from 1.5 to 3 of (-x/3+1)

\int_{1.5}^{3} (- \frac{x}{3} + 1) d x

0.375

Solution steps

\int_{1.5}^{3} - \frac{x}{3} + 1 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_{1.5}^{3} \frac{x}{3} d x + \int_{1.5}^{3} 1 d x

\int_{1.5}^{3} \frac{x}{3} d x = 1.125

\int_{1.5}^{3} 1 d x = 1.5

= - 1.125 + 1.5

Simplify

= 0.375

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What is the integral from 1.5 to 3 of (-x/3+1) ?
The integral from 1.5 to 3 of (-x/3+1) is 0.375