What is the integral from 3 to 9 of sqrt(2x-2)-(x-5) ?

The integral from 3 to 9 of sqrt(2x-2)-(x-5) is 38/3

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integral from 3 to 9 of sqrt(2x-2)-(x-5)

\int_{3}^{9} 2 x - 2 - (x - 5) d x

\frac{38}{3}

Solution steps

\int_{3}^{9} 2 x - 2 - (x - 5) d x

Simplify

= \int_{3}^{9} 2 x - 2 - 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}^{9} 2 x - 2 d x - \int_{3}^{9} x d x + \int_{3}^{9} 5 d x

\int_{3}^{9} 2 x - 2 d x = \frac{56}{3}

\int_{3}^{9} x d x = 36

\int_{3}^{9} 5 d x = 30

= \frac{56}{3} - 36 + 30

Simplify

\frac{56}{3} - 36 + 30 : \frac{38}{3}

= \frac{38}{3}

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What is the integral from 3 to 9 of sqrt(2x-2)-(x-5) ?
The integral from 3 to 9 of sqrt(2x-2)-(x-5) is 38/3