What is the integral from 1 to 16 of (-6x^{-1/2}-4) ?

The integral from 1 to 16 of (-6x^{-1/2}-4) is -96

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integral from 1 to 16 of (-6x^{-1/2}-4)

\int_{1}^{16} (- 6 x^{- \frac{1}{2}} - 4) d x

- 96

Solution steps

\int_{1}^{16} - 6 x^{- \frac{1}{2}} - 4 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_{1}^{16} 6 x^{- \frac{1}{2}} d x - \int_{1}^{16} 4 d x

\int_{1}^{16} 6 x^{- \frac{1}{2}} d x = 36

\int_{1}^{16} 4 d x = 60

= - 36 - 60

Simplify

= - 96

\int_{- 1}^{1} 1 + (- 2 x)^{2} d x

\int_{0}^{1} 3 x^{2} e^{x} d x

\int_{a}^{b} 2 x^{2} d x

\int_{- 2}^{1} (2 - x) - (x^{2}) d x

\int_{12}^{16} (x^{2} - 6)^{\frac{1}{2}} d x

What is the integral from 1 to 16 of (-6x^{-1/2}-4) ?
The integral from 1 to 16 of (-6x^{-1/2}-4) is -96