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 33

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

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

33

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

= 33

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 33