What is the integral from 0 to 6 of sqrt(16-2x)-2 ?

The integral from 0 to 6 of sqrt(16-2x)-2 is 20/3

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integral from 0 to 6 of sqrt(16-2x)-2

\int_{0}^{6} 16 - 2 x - 2 d x

\frac{20}{3}

Decimal

6.66666 \dots

Solution steps

\int_{0}^{6} 16 - 2 x - 2 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_{0}^{6} 16 - 2 x d x - \int_{0}^{6} 2 d x

\int_{0}^{6} 16 - 2 x d x = \frac{56}{3}

\int_{0}^{6} 2 d x = 12

= \frac{56}{3} - 12

Simplify

\frac{56}{3} - 12 : \frac{20}{3}

= \frac{20}{3}

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What is the integral from 0 to 6 of sqrt(16-2x)-2 ?
The integral from 0 to 6 of sqrt(16-2x)-2 is 20/3