What is the integral from 9 to 36 of (sqrt(x)-2) ?

The integral from 9 to 36 of (sqrt(x)-2) is 72

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integral from 9 to 36 of (sqrt(x)-2)

\int_{9}^{36} (x - 2) d x

72

Solution steps

\int_{9}^{36} 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_{9}^{36} x d x - \int_{9}^{36} 2 d x

\int_{9}^{36} x d x = 126

\int_{9}^{36} 2 d x = 54

= 126 - 54

Simplify

= 72

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What is the integral from 9 to 36 of (sqrt(x)-2) ?
The integral from 9 to 36 of (sqrt(x)-2) is 72