What is the integral from-6 to 4 of (-3/2 x+1) ?

The integral from-6 to 4 of (-3/2 x+1) is 25

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integral from-6 to 4 of (-3/2 x+1)

\int_{- 6}^{4} (- \frac{3}{2} x + 1) d x

25

Solution steps

\int_{- 6}^{4} - \frac{3}{2} x + 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_{- 6}^{4} \frac{3}{2} x d x + \int_{- 6}^{4} 1 d x

\int_{- 6}^{4} \frac{3}{2} x d x = - 15

\int_{- 6}^{4} 1 d x = 10

= - (- 15) + 10

Simplify

= 25

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What is the integral from-6 to 4 of (-3/2 x+1) ?
The integral from-6 to 4 of (-3/2 x+1) is 25