What is the integral from-8 to 2 of sqrt(16-6x)-x ?

The integral from-8 to 2 of sqrt(16-6x)-x is 86

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integral from-8 to 2 of sqrt(16-6x)-x

\int_{- 8}^{2} 16 - 6 x - x d x

86

Solution steps

\int_{- 8}^{2} 16 - 6 x - x 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_{- 8}^{2} 16 - 6 x d x - \int_{- 8}^{2} x d x

\int_{- 8}^{2} 16 - 6 x d x = 56

\int_{- 8}^{2} x d x = - 30

= 56 - (- 30)

Simplify

= 86

What is the integral from-8 to 2 of sqrt(16-6x)-x ?
The integral from-8 to 2 of sqrt(16-6x)-x is 86