What is the integral from 9 to 16 of (-x^{-1/2}-5) ?

The integral from 9 to 16 of (-x^{-1/2}-5) is -37

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integral from 9 to 16 of (-x^{-1/2}-5)

\int_{9}^{16} (- x^{- \frac{1}{2}} - 5) d x

- 37

Solution steps

\int_{9}^{16} - x^{- \frac{1}{2}} - 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_{9}^{16} x^{- \frac{1}{2}} d x - \int_{9}^{16} 5 d x

\int_{9}^{16} x^{- \frac{1}{2}} d x = 2

\int_{9}^{16} 5 d x = 35

= - 2 - 35

Simplify

= - 37

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What is the integral from 9 to 16 of (-x^{-1/2}-5) ?
The integral from 9 to 16 of (-x^{-1/2}-5) is -37